Matrices Test

Result

Matrices Test - 2

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Question 1
1 / -0.25

The number of all possible matrices of order 3×3 with each entry 0 if 1 is

A
81

B
512

C
18

D
none of these

Solution

2^3x3 = 2⁹ = 512.

The number of elements in a 3 X 3 matrix is the product 3 X 3=9.

Each element can either be a 0 or a 1.

Given this, the total possible matrices that can be selected is 2⁹=512
Question 2
1 / -0.25

A
A²=A

B
A³ = A

C
A² = O

D
none of these

Solution

If any row or column of a square matrix is 0 , then its product with itself is always a zero matrix.
Question 3
1 / -0.25

This matrix is a _______ .

A
scalar matrix

B
identity matrix

C
diagonal matrix

D
triangular matrix
Question 4
1 / -0.25

Two matrices A and B are multiplicative inverse of each other only if

A
AB = BA

B
AB = O, BA = I

C
AB = BA = O

D
AB = BA = I

Solution

If AB = BA = I , then A and B are inverse of each other. i.e. A is invers of B and B is inverse of A.
Question 5
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For what value of λ the following system of equations does not have a solution ? x + y + z = 6, 4x + λy - λz = 0, 3 x + 2y – 4 z = - 5

A
0

B
3

C
-3

D
1.

Solution

The given system of equations does not have solution if :

⇒ (24 + 6λ - 14λ) = 0 ⇒ λ = 3
Question 6
1 / -0.25

I₂ is the matrix

A

B

C

D

Solution

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by I_n, or simply by I if the size is immaterial or can be trivially determined by the context
Question 7
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Let A be any m×n matrix, then A² can be found only when

A
m < n

B
m = n

C
m > n

D
none of these.

Solution

The product of any matrix with itself can be found only when it is a square matrix.i.e. m = n.
Question 8
1 / -0.25

The order of the single matrix obtained from is

A
2 × 3

B
2 × 2

C
3 × 3

D
3 × 2

Solution
Question 9
1 / -0.25

If A and B are square matrices of the same order, then(A+B)² = A²+2AB+B² implies

A
AB + BA = O

B
AB = O

C
AB = BA

D
none of these.

Solution

If A and B are square matrices of same order , then , product of the matrices is not commutative.Therefore , the given result is true only when AB = BA.
Question 10
1 / -0.25

The value of λ, for which system of equations. x + y + z = 1, x + 2y + 2z = 3, x + 2y + λz = 4, have no solution is

A
1

B
2

C
0

D
3

Solution

The given system of equations does not have solution if :