Free Printable Mock Test_6-2

1.

What are the dimensions of this matrix?

a)

2 x 3

b)

3 x 2

c)

6 x 1

d)

1 x 6

2.

These matrices are being multiplied. Determine the dimension/size of the new matrix.

a)

Can't multiply them

b)

4 x 2

c)

3 x 3

d)

4 x 3

3.

What is the purpose of row operations in solving augmented matrices?

a)

To create a new matrix

b)

To find the determinant of the matrix

c)

To calculate the inverse of the matrix

d)

To simplify and solve the system of equations.

4.

What are the three row operations used to solve augmented matrices?

a)

Interchange two rows, Multiply a row by a non-zero constant, Add a multiple of one row to another row

b)

Swap two rows

c)

Divide a row by a non-zero constant

d)

Subtract a multiple of one row from another row

5.

What in the answer matrix indicates that there is an infinite number of solutions, infinitely many solutions?

a)

the first part of the solution matrix will look like the identity matrix

b)

The solution matrix will be a square matrix

c)

One of the rows in the solution matrix will have all zeros

d)

One of the rows in the solution matrix will have zeros and 1 number.

6.

What in the answer matrix indicates that there is no solution?

a)

the first part of the solution matrix will look like the identity matrix

b)

The solution matrix will be a square matrix

c)

One of the rows in the solution matrix will have all zeros

d)

One of the rows in the solution matrix will have zeros and 1 number.

7.

Reduced Row Echelon Form is where ______________________

a)

Zeroes in the first column of my matrix

b)

Thel ast column has all zeroes

c)

One's are in a diagonal pattern of my matrix with zeroes underneath the one's.before the augmented portion

d)

One's are in a diagonal pattern of my matrix with zeroes above and below the ones before the augmented portion

8.

What is the difference between row echelon form and reduced row echelon form?

a)

The row echelon form allows for leading coefficients other than 1.

b)

The reduced row echelon form does not require the leading coefficient to be 1.

c)

The difference between row echelon form and reduced row echelon form is that the reduced row echelon form has the additional condition that the leading coefficient of each nonzero row is always 1.

d)

The row echelon form has more strict conditions for zero rows than the reduced row echelon form.

9.

This is an example of

a)

Row Echelon Form

b)

Reduced Row Echelon Form

c)

Really Reduced Echelon Form

d)

Really Really Easy Form

10.

This is an example of a

a)

System of Quadratic Equations

b)

Reduced Row Echelon Form

c)

Augmented Matrix

d)

A Canine Doing a Backflip

11.

Solve, if possible.

x - y + 2z = -1

-3x + 3y + 5z = 3

2x - 2y = -2

a)

x = 1, y = 1, z = 4

b)

No solution

c)

Infinitely many solutions

d)

x = -1, y = -1, z = 4

12.

Solve, if possible.

2x + 5y + z = -12

-x + 4y + 3z = -4

5x - 2z = -13

a)

x = 3, y = 1, z = 1

b)

No solution

c)

Infinitely many solutions

d)

x = -3, y = -1, z = -1

13.

Solve, if possible.

3x + 3y = -12

-4x - 2y + 2z = -14

x + 3y + 2z = 11

a)

x = 1, y = 1, z = 4

b)

No solution

c)

Infinitely many solutions

d)

x = -1, y = -1, z = 4

14.

Solve, if possible.

4x - 2y = 2

5x - 2y + z = 7

3x + 4y - z = 3

a)

x = 1, y = 1, z = 4

b)

No solution

c)

Infinitely many solutions

d)

x = -3, y = -1, z = -1

15.

Which system matches the augmented matrix shown?

a)

2x+y+2z=2
3x+5y-z=4
x-2y-3z=6

b)

x+y+z=2
3x-5y-z=4
x+2y-3x=6

c)

2x-2z+y=2
3x-5y+z=-4
x-2y-3z=6

d)

2x+y+2z=2
3x-5y-z=4
x-2y-3z=-6

16.

What is the solution to the 4x5 Matrix?

a)

( 3, 4, 9, 6 )

b)

( 3, 4, 9, -6 )

c)

( -6, 9, 4, 3 )

d)

( 6, 9, 4, 3 )

17.

What is the solution to the systems of equations represented by the 3x4 Matrix?

a)

(4, 6, 2)

b)

(-6, 2, 2)

c)

All Real Numbers

d)

No Solutions

18.

a)

(2,3,5,0)

b)

(2,3,4,5)

c)

All Real Numbers

d)

No Solution

19.

Using back-substitution, calculate the solution for the REF matrix.

a)

(3, -6, 3)

b)

(-6, -6, 3)

c)

(6, -6, 3)

d)

(-6, -6, 3)

20.

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation?

a)

x + y = 6
14.80x + 17y = 91

b)

x + y = 91
14.80x + 17y = 6

c)

x + y = 6
14.80y + 17x = 91

d)

x + y = 91
14.80x+ 17y = 6

21.

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80 and some order steak for $17. If the total bill was $91, how many of each kind of dinner was purchased?

a)

3 chicken, 3 steak

b)

5 chicken, 1 steak

c)

1 chicken, 5 steak

d)

4 chicken, 2 steak

22.

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. How many of each type of ticket were sold?

a)

10 adults, 11 children

b)

12 adults , 9 children

c)

11 adults, 10 children

d)

9 adults, 12 children

23.

Johnny was using Gaussian Elimination to simplify the matrix. What did he do wrong in this step?

a)

To get a zero for a number you should multiply the same row by its' reciprocal

b)

If you multiply a number to a row you have to change that row too

c)

He added the numbers incorrectly

d)

Nothing. This step was correct.

24.

Jessica is simplifying the matrix using Gaussian Elimination. Did she complete the step correctly?

a)

No, she should have changed the 2 to a zero and multiplied -2 by R2 and added R1

b)

No, she wanted to change the 3 to a zero so she should have multiplied R2 and added it to R3

c)

Yes. When you need a zero you multiply by the number's reciprocal.

d)

No. Just punch in the calculator. Who cares about Carl Gauss

25.

Please draw how you feel about Systems of Linear Equations on the big bird scale :)

🐤🐥

26.

Find the determinant of the matrix

a)

A

b)

B

c)

C

d)

D

27.

Find the inverse of the matrix

a)

A

b)

B

c)

C

d)

D

28.

Find the determinant of the matrix

a)

A

b)

B

c)

C

d)

D

29.

Find the inverse of the matrix

a)

A

b)

B

c)

C

d)

D

30.

Dimensions?

a)

a

b)

b

c)

c

d)

d

31.

Element Address?

a)

a

b)

b

c)

c

d)

d

32.

a)

17 12
25 18

b)

8 9
12 6

c)

6 6
7 5

d)

12 10
10 12

33.

a)

b)

c)

d)

34.

Multiply

a)

20 15 -10
30 -5 0

b)

-20 15 -10
30 -5 0

c)

1 8 3
11 4 5

d)

20 -15 10
-30 5 0

35.

Evaluate the determinant of the matrix.

a)

40

b)

30

c)

20

d)

10

36.

If A and B are invertible matrix then (AB)^-1 =

a)

A^-1B^-1

b)

AB

c)

B^-1A^-1

d)

none of these

37.

1. Let A be a square matrix of order 3x3 then| kA| = .

a)

k |A|

b)

k²|A|

c)

k³|A|

d)

3k|A|

38.

When you multiply a matrix by the identity matrix, you obtain the

a)

inverse matrix.

b)

transpose matrix.

c)

Identity matrix

d)

original matrix.

39.

If |A| = 0, then A is

a)

zero matrix

b)

singular matrix

c)

non-singular matrix

d)

Identity matrix

40.

Find the inverse of the matrix

a)

A

b)

B

c)

C

d)

D

41.

a)

5 -2
-3 1

b)

-5 2
3 -1

c)

-5 3
2 -1

d)

1 -3
-2 5

42.

Calculate the determinant

a)

0

b)

none

c)

-32

d)

-8

43.

a)

9a

b)

9

c)

18a

d)

18

44.

a)

-96

b)

96

c)

-3

d)

-12

45.

If the order of matrix A is m×p. And the order of B is p×n. Then the order of matrix AB is

a)

m × n

b)

n × p

c)

n × m

d)

m × p

46.

What do we call this notation $\left|\ \right|$ ?

a)

absolute value notation

b)

Straight line notation

c)

horizontal line notation

d)

vertical line notation

47.

We can calculate the determinant of the following orders except?

a)

2x2

b)

3x3

c)

2x3

d)

4x4

48.

What are the operations used in calculating the determinant of a matrix?

a)

Addition & Subtraction

b)

Multiplication & Subtraction

c)

Multiplication & Addition

d)

Multiplication & Division

49.

What's the formula in calculating the determinant of a matrix?

a)

ab-dc

b)

ab+dc

c)

ad+bc

d)

ad-bc

50.

Which of the following is the correct equation to get the determinant of the given matrix?

a)

3(2) - 1(5)

b)

3(1) - 2(5)

c)

3(2) + 1(5)

d)

3(1) + 2(5)

51.

Find the magnitude of the vector <2, -3>.

a)

√11

b)

13

c)

√-4

d)

√13

52.

Find the direction of the vector <-3, -5>.

a)

59.03°

b)

239.03°

c)

210.96°

d)

120.96°

53.

Find the dot product of <1, -2> and <3, 2>.

a)

1

b)

<3, -4>

c)

<4, 0>

d)

-1

54.

Find the angle between vectors <1,3> and <2,-5>.

a)

40.24°

b)

49.76°

c)

139.76°

d)

92.57°

55.

How do you know if two vectors are orthogonal?

a)

Their sum is 0.

b)

The dot product is 1.

c)

The angle between them is 0°.

d)

The dot product is 0.

56.

the direction (θ) for vector v. Round to three decimals.

a)

-74.054^o

b)

105.945^o

c)

-15.945^o

d)

164.055^o

57.

Find the angle between u and v.

a)

78.930^o

b)

33.691^o

c)

101.070^o

d)

146.310^o

58.

Find the unit vector in the same direction as v.

a)

<0.385, 0.923>

b)

<-0.832, 0.555>

c)

<5/13, 12/13>

d)

<-5/13, -12/13>

59.

Given an initial point R ( -12, 4 ) and terminal point S ( 28, -17 ), find the component form of the vector RS.

a)

〈14,-13〉

b)

〈-14,13〉

c)

〈-40,-21〉

d)

〈40,-21〉

60.

Given an initial point A ( 2, 4 ) and terminal point B ( -8, 7 ), find the component form of the vector AB.

a)

〈-10,3〉

b)

〈-6,3〉

c)

〈10,11〉

d)

〈-6,-3〉

61.

Determine the direction and magnitude of the vector 〈-11,5〉

a)

Direction 24.4°
Vertical 12.1

b)

Direction65.6°
Magnitude 12.1

c)

Direction -24.4°
Magnitude 12.1

d)

Direction 155.6°
Magnitude 12.1

62.

Determine the direction and magnitude of the vector 〈7,18〉

a)

Direction 21.3°
Magnitude 19.3

b)

Direction 68.7°
Magnitude 19.3

c)

Direction 21.3°
Magnitude 373

d)

Direction 68.7°
Magnitude 373

63.

Given u = <3, 7> and v =<-5, 4>, find 2u - 3v

a)

<21, 2>

b)

<-11, 26>

c)

<8, 3>

d)

23

64.

Given u = <3, 7> and v =<-5, 4>, find 2v - 3u

a)

<21, 2>

b)

<-19, -13>

c)

<-15, 3>

d)

23

65.

Find the magnitude of the vector <10, -8>

a)

2

b)

12.81

c)

6

d)

18

66.

Find the magnitude of the vector <5, 5>

a)

0

b)

10

c)

25

d)

7.07

67.

Find the direction angle for the vector <-8, 3>

a)

159.44°

b)

200.56°

c)

110.56°

d)

249.44°

68.

Find the unit vector in the direction of <4, -3>

a)

<⅘, -⅗>

b)

<0.57, -0.43>

c)

<1, -1>

d)

-¾

69.

A vector is a mathematical structure that has both _______ and _______.

a)

direction, magnitude

b)

scope, sequence

c)

meat, potatoes

d)

scalar, vector

70.

State the transformation of $f\left(x\right)$ notated by $f\left(x\right)\ +2$

a)

Vertical Shift Up 2

b)

Vertical Shift Down 2

c)

Horizontal Shift left 2

d)

Horizontal shift right 2

71.

State the transformation of $f\left(x\right)$ notated by $f\left(x-2\right)$

a)

Vertical Shift Up 2

b)

Vertical Shift Down 2

c)

Horizontal Shift left 2

d)

Horizontal shift right 2

72.

State the transformation of $f\left(x\right)$ notated by $f\left(x+2\right)$

a)

Vertical Shift Up 2

b)

Vertical Shift Down 2

c)

Horizontal Shift left 2

d)

Horizontal shift right 2

73.

State the transformation of $f\left(x\right)$ notated by $f\left(x\right)-2$

a)

Vertical Shift Up 2

b)

Vertical Shift Down 2

c)

Horizontal Shift left 2

d)

Horizontal shift right 2

74.

State the transformations from f(x) to g(x):

$f\left(x\right)=\frac{1}{3}x+3;\ \ \ \ \ g\left(x\right)\ =f\left(x\right)-3$

a)

Vertical Shift Up 3

b)

Vertical Shift Down 3

c)

Horizontal Shift Left 3

d)

Horizontal Shift Right 3

75.

State the transformations from f(x) to g(x):

$f\left(x\right)=-3x+4;\ \ \ \ \ g\left(x\right)\ =f\left(x\right)+1$

a)

Vertical Shift Up 1

b)

Vertical Shift Down 1

c)

Horizontal Shift Left 1

d)

Horizontal Shift Right 1

76.

State the transformations from f(x) to g(x):

$f\left(x\right)=-\frac{1}{2}x-5;\ \ \ \ \ g\left(x\right)\ =f\left(x-3\right)$

a)

Vertical Shift Up 3

b)

Vertical Shift Down 3

c)

Horizontal Shift Left 3

d)

Horizontal Shift Right 3

77.

State the transformations from f(x) to g(x):

$f\left(x\right)=\frac{2}{3}x+1;\ \ \ \ \ g\left(x\right)\ =3f\left(x\right)$

a)

Vertical Shift Up 3

b)

Horizontal Shift up 3

c)

Vertical Stretch by a factor of 3

d)

Vertical Shrink by a factor of 3

78.

State the transformations from f(x) to g(x):

$f\left(x\right)=\frac{2}{3}x+1;\ \ \ \ \ g\left(x\right)\ =4f\left(x\right)$

a)

Vertical Shift Up 4

b)

Horizontal Shift up 4

c)

Vertical Stretch by a factor or 4

d)

Vertical Shrink by a factor of 4

79.

State the transformations from f(x) to g(x):

$f\left(x\right)=3x-12;\ \ \ \ \ g\left(x\right)\ =\frac{1}{6}f\left(x\right)$

a)

Vertical Stretch by 6

b)

Vertical Shrink by 6

c)

Vertical Stretch by a factor or $\frac{1}{6}$

d)

Vertical Shrink by a factor of $\frac{1}{6}$

80.

State the transformations from f(x) to g(x):

$f\left(x\right)=4x+8;\ \ \ \ \ g\left(x\right)\ =\frac{3}{4}f\left(x\right)$

a)

Vertical Stretch by $\frac{4}{3}$

b)

Vertical Shrink by $\frac{4}{3}$

c)

Vertical Stretch by a factor or $\frac{3}{4}$

d)

Vertical Shrink by a factor of $\frac{3}{4}$

81.

State the transformations from f(x) to g(x):

$f\left(x\right)=x-2;\ \ \ \ \ g\left(x\right)\ =\frac{1}{4}f\left(x\right)$

a)

Vertical Stretch by 4

b)

Vertical Shrink by 4

c)

Vertical Stretch by a factor or $\frac{1}{4}$

d)

Vertical Shrink by a factor of $\frac{1}{4}$

82.

State the transformations from f(x) to g(x):

$f\left(x\right)=4x+8;\ \ \ \ \ g\left(x\right)\ =-f\left(x\right)$

a)

Vertical Shift down 1

b)

Horizontal Shift Right 1

c)

Reflection over the x-axis

d)

Reflection over the y-axis

83.

State the transformation of f(x) to g(x):

$f\left(x\right)=-2x-7;\ \ \ g\left(x\right)=f\left(x-2\right)$

a)

Vertical Shift Up 2

b)

Vertical Shift Down 2

c)

Horizontal Shift left 2

d)

Horizontal shift right 2

84.

Write a new function g(x) to represent the transformation of f(x):

$f\left(x\right)=-3x+4\ \ \ \ to\ \ \ \ g\left(x\right)=f\left(x\right)+1$

a)

$g\left(x\right)=-3x\ +\ 3$

b)

$g\left(x\right)=-3x+5$

c)

$g\left(x\right)=-3x+1$

d)

$g\left(x\right)=-3x+7$

85.

Write a new function g(x) to represent the transformation of f(x):

$f\left(x\right)=-3x+4\ \ \ \ to\ \ \ \ g\left(x\right)=f\left(x+1\right)$

a)

$g\left(x\right)=-3x\ +\ 3$

b)

$g\left(x\right)=-3x+5$

c)

$g\left(x\right)=-3x+1$

d)

$g\left(x\right)=-3x+7$

86.

Write a new function g(x) to represent the transformation of f(x):

$f\left(x\right)=-2x\ +\ 1\ \ \ \ to\ \ \ \ g\left(x\right)=-f\left(x\right)$

a)

$g\left(x\right)=2x-1$

b)

$g\left(x\right)=2x+1$

c)

$g\left(x\right)=-2x+1$

d)

$g\left(x\right)=-2x-1$

87.

The transformation $y=f\left(x-h\right)$ is what type of transformation?

a)

Vertical Stretch

b)

Vertical Shrink

c)

Reflection

d)

Horizontal Translation

e)

Vertical Translation

88.

The transformation $y=f\left(x\right)+k$ is what type of transformation?

a)

Vertical Stretch

b)

Vertical Shrink

c)

Reflection

d)

Horizontal Translation

e)

Vertical Translation

89.

The transformation $y=a\cdot f\left(x\right)$ , when $a>1$ , is what type of transformation?

a)

Vertical Stretch

b)

Vertical Shrink

c)

Reflection

d)

Horizontal Translation

e)

Vertical Translation

90.

If A is a square matrix Ax=λx for nonzero scalar λ, then x is an eigenvector of A

a)

True

b)

False

91.

If λ is an eigenvalue of matrix A, then linear system (A-λI)v=0 has only trivial solution.

a)

True

b)

False

92.

If λ is an eigenvalue of matrix A, then the eigenspace of A corresponding to λ is the set of eigenvectors of A corresponding to λ

a)

True

b)

False

93.

If 0 is an eigenvalue of a matrix A, then A² is singular

a)

True

b)

False

94.

The eigenvalues of matrix A are the same as the eigenvalues of RREF of A

a)

True

b)

False

95.

If 0 is an eigenvalue of matrix A, then the set of columns of A is linearly independent

a)

True

b)

False

96.

Find eigenvalues for matrix A

a)

λ=1,3

b)

λ=-1,2

c)

λ=1,-2

d)

λ=1,4

97.

Find the eigenvectors for matrix A corresponding to the smallest eigenvalue.

a)

v={r(0,2),r∊R, r≠0}

b)

v={r(1,0),r∊R, r≠0}

c)

v={r(0,1),r∊R, r≠0}

d)

v={r(1,2),r∊R, r≠0}

98.

Find the dimension of eigenspace/geometric multiplicity for matrix A.

a)

1

b)

2

c)

3

d)

4

99.

Find the eigenvalues for A⁹ of matrix A

a)

λ=1,1/8,512

b)

λ=1,1/2,2

c)

λ=1,1/512,512

d)

λ=1,0,512

100.

Find the eigenvalues A^T and A^-1 of matrix A

a)

A^T: λ=1,4,7
A^-1: λ=1,1/4,1/7

b)

A^T: λ=1,5,9
A^-1: λ=1,1/5,1/9

c)

A^T: λ=0,5,8
A^-1: λ=0,1/5,1/8

d)

A^T: λ=1,0,0
A^-1: λ=undefined

101.

The dot product and innerproduct are same on the space $R^n$

a)

True

b)

False

102.

Let W be the subspace of $R^3$ spanned by $x=\left(1,-5,0\right)$ . The unit vector u that is a basis for W is

a)

$\left(\frac{1}{\sqrt[]{26}},\frac{-5}{\sqrt[]{26}},0\right)$

b)

$\left(\frac{1}{\sqrt[]{27}},\frac{-5}{\sqrt[]{27}},0\right)$

c)

$\left(1,0,0\right)$

d)

$\left(0,1,0\right)$

103.

Two vectors u and v are orthogonal if and only if

a)

$\parallel u+v\parallel^2=\parallel u\parallel^2-\parallel v\parallel^2$

b)

$\parallel u-v\parallel^2=\parallel u\parallel^2+\parallel v\parallel^2$

c)

$\parallel u\parallel^2+\parallel v\parallel^2=\parallel u+v\parallel^2$

d)

$\parallel u\parallel^2-\parallel v\parallel^2=\parallel u-v\parallel^2$

104.

Let $V=R^3$ and W be two dimensional subspace of $R^3$ , the plane containing the origin. Also let L be the line through the origin and perpendicular to W. Then the orthogonal complement of W is

a)

$L$

b)

$L^{\perp}$

c)

$\left\{\left(0,0,0\right)\right\}$

d)

None of these

105.

Let A be a $10\times10$ matrix. Then the orthogonal complement of $Col\ A$ is

a)

$Nul\ A$

b)

$Row\ A$

c)

$Row\ A^T$

d)

$Nul\ A^T$

106.

Find a basis for the Orthogonal Complement of the row space of B

4 lines

107.

What is the exponent form for
6?

a)

6⁰

b)

6¹

108.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

109.

-3 + (-4)

a)

12

b)

-7

c)

-1

d)

1

110.

-6 - (-4)

a)

-10

b)

2

c)

-2

d)

10

Mock Test_6-2_Linear Algebra

Total questions: 110

Worksheet time: 6hrs 30mins

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