Free Printable Midterm in Linear Algebra

1.

How many solutions will this system have?

a)

No solution

b)

One Solution

c)

I Don't Know

d)

Infinitely Many Solutions

2.

A system of linear equations can be consistent and independent. This is a system of linear equations having infinitely many solution. The slopes of the lines defined by the equations are equal, their y-intercepts are also equal.

a)

System of linear equation in two variables

b)

Consistent and Independent

c)

Consistent and Dependent

d)

Inconsistent

3.

This is a system of linear equations having no solution. The slopes of the lines defined by the equations are equal but their y-intercepts are not equal.

a)

System of linear equation in two variables

b)

Consistent and Independent

c)

Consistent and Dependent

d)

Inconsistent

4.

Which statement are true regarding the following system of linear equation?

$x_{1\ }-\ 2x_{2\ }-x_{3\ }+3x_4=0$

$-2x_1+4x_2+5x_3-5x_4=3$

$3x_1-6x_2-6x_3+8x_4=2$

a)

The system is inconsistent

b)

The system has no free variables

c)

The system has infinitely many solution

d)

The system has 3 basic variables

5.

Which statement are true regarding the following system of linear equation?

$x_{1\ }+\ 2x_{2\ }+\ 4x_{3\ }=\ 5$

$2x_{1\ }+\ 4x_{2\ }+\ 5x_{3\ }=\ 4$

$4x_{1\ }+\ 5x_{2\ }+\ 4x_{3\ }=\ 2$

a)

The system is inconsistent.

b)

The system has one unique solution

c)

The system has free variables

d)

The system has infinitely many general solution

e)

The system has 3 basic variables.

6.

Find the product of the two matrices.

a)

undefined

b)

-3 16
17 12
8 -10

c)

3 12
-15 -8
-1 -3

7.

find: B*A

a)

47 30
9 5

b)

17 15
42 35

c)

10 25
7 1

d)

not possible because rows do not match columns

8.

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

9.

Perform scalar multiplication on the matrix

a)

A

b)

B

c)

C

d)

D

10.

a)

b)

c)

d)

11.

What are the dimensions of this matrix?

a)

2 x 3

b)

3 x 2

c)

6 x 1

d)

1 x 6

12.

Find B-A

a)

-3 1
7 -1

b)

1 0
1 -4

c)

4 0
-6 0

d)

not possible because rows do not match columns

13.

Find A+B

a)

8 10
8 1

b)

12 25
7 1

c)

10 30
0 1

d)

can't add two together because the rows dont match columns

14.

$x+2y+z=2$

$3x+8y+z=12$

$4y+z=2$

for the system of equations above:

a)

x=-2,y=1,z=-2

b)

x=2,y=1,z=2

c)

x=2,y=1,z=-2

d)

x=-2,y=-1,z=-2

15.

Find V + X

a)

b)

c)

d)

Does Not Exist

16.

Find Z - W

a)

b)

c)

d)

Does Not Exist

17.

Find (W + Y) - V

a)

b)

c)

d)

Does Not Exist

18.

Perform the matrix multiplication, if possible.

a)

b)

c)

d)

Cannot be multiplied, dimensions not compatible.

19.

Perform the matrix multiplication, if possible.

a)

b)

c)

d)

Cannot be multiplied, dimensions not compatible.

20.

What is a Matrix?

a)

An equation of over 5 numbers or symbols

b)

A set of numbers in rows and columns

c)

A method of finding the n^th value of a series

d)

A complicated number system

21.

In matrices (AB)^t equals to

a)

B

b)

A

c)

A^t B^t

d)

B^t A^t

22.

If A is a 3×3 non-singular matrix such that $AA^T=A^TA$ and $B=A^{-1}A^T$ , then $BB^T$ =

a)

$A$

b)

$B$

c)

$I_3$

d)

$B^T$

23.

a)

b)

c)

d)

24.

$IfA^TA^{-1}\ is\ symmetric,\ then\ A^2=$

a)

$A^{-1}$

b)

$\left(A^T\right)^2$

c)

$A^T$

d)

$\left(A^{-1}\right)^2$

25.

•Determinant of a skew-symmetric matrix of odd order is always

a)

1

b)

0

c)

-1

d)

May be any number

26.

•Determinant of an orthogonal matrix of any order is always

a)

1 or-1

b)

0

c)

2 or -2

d)

may be any number

27.

•For a system of n linear homogeneous equations to be have non-trivial solution must have

a)

|A| must be negative

b)

•|A| must be positive

c)

•|A| must be equal to zero.

d)

•No condition on |A|.

28.

a)

1

b)

2

c)

3

d)

0

29.

What must be true in order to ADD two matrices?

a)

They must be square.

b)

The dimensions must be equal.

c)

The determinant can't equal 0.

d)

The column of the 1st must equal the row of the 2nd.

30.

What must be true in order to MULTIPLY two matrices?

a)

They must be square.

b)

The dimensions must be equal.

c)

The determinant can't equal 0.

d)

The #of columns of the 1st must equal the # of rows of the 2nd.

31.

Calculate the determinant

a)

0

b)

-15

c)

-70

d)

10

32.

Which of the following matrices has an inverse of ⌈−⅗ ⅘⌉
⌊⅖ −⅕⌋ ?
*det = -5

a)

⌈1 2⌉
⌊3 4⌋

b)

⌈1 3⌉
⌊2 4⌋

c)

⌈1 4⌉
⌊2 3⌋

d)

⌈−3 4⌉
⌊2 −1⌋

33.

By solving Simultaneous linear algebraic equation in which method we have to use back substitution concept.

a)

Gauss Jacobi method

b)

Gauss Seidal Method

c)

Gauss elimination method

d)

Gauss Jordan Method

34.

This is an example of

a)

Row Echelon Form

b)

Reduced Row Echelon Form

c)

Really Reduced Echelon Form

d)

Really Really Easy Form

35.

Reduced Row Echelon Form is where ______________________

a)

Zeroes in the first column of my matrix

b)

The last 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

36.

Gauss Elimination Method & Gauss Jordan Methods are _______ methods

a)

Direct

b)

Indirect.

c)

Self- correcting

d)

Step by step

37.

This is an example of a/an

a)

System of Quadratic Equations

b)

Reduced Row Echelon Form

c)

Augmented Matrix

d)

A Canine Doing a Backflip

38.

Aina 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

39.

Farah solved the matrix on the left. Ibrahim solved the matrix on the right. Who is correct?

a)

Farah, because she multiplied by the reciprocal.

b)

Ibrahim, because he got the top left number to be a one.

c)

Neither. They needed to take care of the one and make it a zero first.

d)

Both. Each step is legal and takes care of the top left term

40.

In Gauss Jordan method which of the following transformations are allowed?

a)

Diagonal transformation

b)

Square transformation

c)

Row transformation

d)

Column transformation

41.

a)

b)

c)

d)

42.

a)

1

b)

0

c)

a + b + c

d)

3abc

43.

a)

0

b)

1

c)

-1

d)

$\frac{\sqrt{3}}{2}$

44.

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

a)

A^-1B^-1

b)

AB

c)

B^-1A^-1

d)

none of these

45.

a)

b)

c)

d)

46.

Which of the following is not true

a)

If any two rows / columns of a determinant are identical then the value of determinant is zero.

b)

If each element of a row / column of a determinant is multiplied by the same number k , then value of the new determinant is k times the value of original determinant.

c)

If A and B are square matrices of same order then |AB| = |A|.|B|

d)

If A is a square matrix then |A| = the sum of the products elements of any row/column with the cofactors of the corresponding elements of some other row/column

47.

Which of the following is true

a)

If any two rows / columns are interchanged then value of the determinant remains unchanged.

b)

If any two rows/ columns are interchanged then value of the determinant becomes two times.

c)

If any two rows / columns are interchanged then value of the determinant changes by minus sign.

d)

If any two rows/ columns are interchanged then value of the determinant becomes zero.

48.