Quiz about Matrices & Eigen values

Question 1

No Calculator

Accepted Answer

Question 2

No Calculator

Accepted Answer

Question 3

Calculator Allowed

Accepted Answer

Question 4

Calculator Allowed

Accepted Answer

Question 5

No Calculator

Accepted Answer

Question 6

Calculator Allowed

Accepted Answer

Question 7

No Calculator Allowed

Accepted Answer

Question 8

find: B*A

Accepted Answer

47 30 9 5

Answer

17 15
42 35

Answer

10 25 7 1

Answer

not possible because rows do not match columns

Question 9

What do w, x, y and z equal in this matrix subtraction?

Accepted Answer

w = 13, x = 4, y = 11, z = 23

Answer

w = 13, x = 4, y = 7, z = 23

Answer

w = 13, x = -4, y = 11, z = 23

Answer

w = 13, x = 4, y = 11, z = 17

Question 10

Calculate the determinant

Accepted Answer

0

Answer

none

Answer

-32

Answer

-8

Question 11

Calculate the determinant

Accepted Answer

10

Answer

0

Answer

-15

Answer

-70

Question 12

Which matrix equation represents this system of equations?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 13

Calculate the determinant for the above matrix.

Accepted Answer

6

Answer

16

Answer

-16

Answer

-6

Question 14

Solve system by using Cramer's Rule. Answers are written in the following form (x,y)
$$4x+6y=3$$
$$8x-3y=1$$

Accepted Answer

$$\left(\frac{1}{4},\frac{1}{3}\right)$$

Answer

$$\left(-\frac{1}{3},\frac{1}{4}\right)$$

Answer

$$\left(\frac{1}{3},\frac{1}{4}\right)$$

Answer

$$\left(\frac{1}{4},-\frac{1}{3}\right)$$

Question 15

Which row command is an appropriate next step?

Accepted Answer

-7R2 + R3 -> R3

Answer

7R2 + R3 -> R3

Answer

-7R1 + R3 -> R3

Answer

7R3 -> R3

Question 16

What is the value of z?

Accepted Answer

6

Answer

-6

Answer

-36

Answer

4

Question 17

What is an appropriate first row command to solve this by Gaussian Elimination?

Accepted Answer

-2R1 + R2 -> R2

Answer

2R2 + R2 -> R2

Answer

R3 +R2 --> R3

Answer

2R1 + R2 --> R2

Question 18

What is the value of y?

Accepted Answer

3

Answer

7

Answer

-1

Answer

2

Question 19

What is the value of x in this system?

Accepted Answer

2

Answer

3

Answer

-1

Answer

7

Question 20

What is the solution to this system?

Accepted Answer

{(2, 3, -1)}

Answer

{(3, -1, 2)}

Answer

{(-1, 3, 2)}

Answer

{(2, -1, 3)}

Question 21

Write the equation as an augmented matrix.

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 22

Which rule is not correct for Gaussian elimination?

Accepted Answer

Add/Subtract a number to a row.

Answer

Multiple rows by constant.

Answer

Add/Subtract rows with rows.

Answer

Divide by a constant

Answer

Swap rows

Question 23

The Eigen values of the given matrix are 1,1,2 then the eigen values of its inverse are _______

Accepted Answer

1,1,0.5

Answer

0.5,0.5,0.5

Answer

1,1,1

Answer

1,1,0

Question 24

If the eigen values of 3X3 matrix is 2,5,3 then find detA

Accepted Answer

30

Answer

40

Answer

50

Answer

20

Question 25

If the Eigen values of A are 3,4,5 then Eigen values of square of A

Accepted Answer

9,16,25

Answer

16,25,9

Answer

1/3,1/4,1/5

Answer

25,16,9

Question 26

What is the trace of A= [ 2 3 6 ; -9 0 8 ; 6 2 3]

Accepted Answer

5

Answer

4

Answer

-4

Answer

-5

Question 27

If the sum of two eigen values and trace of a 3 x 3 matrix are equal then the determinant value of the matrix is ________

Accepted Answer

0

Answer

1

Answer

-1

Question 28

Find the sum of Eigen values of the matrix

Accepted Answer

7

Answer

6

Answer

5

Answer

4

Question 29

If -1, 2, 3 are Eigen values of the matrix A then find the Eigen values of the matrix A³.

Accepted Answer

-1, 8, 27

Answer

-1, 6, 9

Answer

-1, 2, 3

Answer

-1, 1/2, 1/3

Question 30

If (1, 3, 4) are the Eigen values of the matrix A, then find Eigen values of 2A.

Accepted Answer

(2, 6, 8)

Answer

(1, 9, 16)

Answer

(1, 3, 4)

Answer

(1, 1/3, 1/4)

Question 31

The Eigen values of the matrix ------ and ----- are the same.

Accepted Answer

A & AT

Answer

A & A-1

Answer

A & A2

Answer

A & -A

Question 32

If the characteristic equation of a matrix is $$\lambda^3-7\lambda^2+36=0$$ , then find the Eigen values of the matrix.

Accepted Answer

(-2, 3, 6)

Answer

(1, 2, 3)

Answer

(2, 3, 6)

Answer

(-1, 2, 3)

Question 33

Every square matrix satisfies it's own --------

Accepted Answer

characteristic equation

Answer

equation

Answer

polynomial equation

Answer

cubic equation

Question 34

If the Eigen values are 0,1,2 then nature is

Accepted Answer

Semi positive definite

Answer

Positive definite

Answer

Negative definite

Answer

Indefinite

Question 35

If the Eigen values are -2,0 then nature of quadratic form is

Accepted Answer

Semi negative

Answer

Positive

Answer

Semi positive

Answer

Negative

Question 36

The number of positive square terms in the canonical form is called the ___ of the quadratic form.

Accepted Answer

index

Answer

signature

Answer

rank

Answer

quadratic form

Question 37

A homogeneous polynomial of the second degree in any number of variables is called a__.

Accepted Answer

quadratic form

Answer

ssignature

Answer

index

Answer

rank

Question 38

If all the eigen values are positive then the nature of the quadratic form is ___

Accepted Answer

Positive definite

Answer

Negative definite

Answer

Indefinite

Answer

Positive semidefinite

Question 39

__________ eigenvector is found out by dividing each element by magnitude of column vector.

Accepted Answer

Normalized

Answer

Model

Answer

signature

Answer

index

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