Matrices Test

Result

Matrices Test - 13

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Question 1
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Let P, Q & R are the matrices of the same order where Q^T & P^T are transpose of matrices Q & P respectively. Choose the correct answer

A
P + Q = Q + P^T

B
Q + R = P + Q

C
P + (Q + R) = (P + Q) + R

D
P^T + (Q + R) = (P + Q^T) + R

Solution

As we know the properties of matrices for A, B, & C square matrices

(i) A + B = B + A (Commutative law)

(ii) (A + B) + C = A + (B + C) (Associative law)

(iii) A + O = O + A = A

Where ,

O = Zero matrix

= additive identity.

(iv) A + (-A) = 0 = (-A) + A

Where,

A = additive inverse obtained by taking neg. sign to A.

So, According to question

(iii) P + (Q + R) = (P + Q) + R (Associative law)
Question 2
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Let A.B and C are the square matrices of the same order. Choose the correct option on which Associative law holds.

A
AB = AC (B = C)

B
A(B + C) = AB + AC

C
(A + B) C = AC + BC

D
(AB) C = A (BC)

Solution

Properties of matrices. AB ≠ BA (Generally not commutative)

(AB) C = A (BC) = ABC (Associative)

A(B + C) = AB + AC (Distributive law)

(A + B) C = AC + BC (Dsitributive law)

Here,

According to question,

(iv) (AB) C = A (BC) (Associative law)