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Question

Consider two matrices A and B. (A+B)T = __________



Your Answer
A

(AB)T 

Your Answer
B

AB

Correct Answer
C

AT + BT

Your Answer
D

BA


Solution

The correct option is C

AT + BT


(A+B)T  = (A)T +​ (B)T 

The matrix obtained by interchanging the rows and columns of a matrix is said to be the transpose of that matrix.

Consider an example 

A = [1223] and B = [4120]

A + B = [5343]

(A + B)T = [5433]

AT = [1223] and BT = [4210]

AT + BT = [5433]

Therefore, (A + B)T = AT + BT.

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