ISRO2009-62

Question

If $\text{A, B, C}$ are any three matrices, then $\text{A}'+\text{B}'+\text{C}' $ is equal to

• A. a null matrix
• B. $\text{A + B + C}$
• C. $\text{(A + B + C)}'$
• D. $\text{-(A + B + C})$

Comments

When in doubt, take small matrices and verify by option elimination.

Answer 1

Here A^' is the Transpose Matrix also written A^t , A^{tr ,} t_A  ,A^t  .

We knows Transpose respect addition

A^' + B^' + C^' =( A + B + C)^'  

Hence,Option(C) ( A + B + C)^'  is the correct choice.

Answer 2

Suppose you forget properties of transpose at exam time, you can quickly solve such questions using simple examples:

Let A= $\begin{bmatrix} 1\\2 \end{bmatrix}$ B= $\begin{bmatrix} 3\\4  \end{bmatrix}$ and C= $\begin{bmatrix} 5\\6 \end{bmatrix}$

A'+B'+C'= $\begin{bmatrix} 1 & 2 \end{bmatrix}$ + $\begin{bmatrix} 3 & 4 \end{bmatrix}$ +$\begin{bmatrix} 5 & 6 \end{bmatrix}$  =$\begin{bmatrix} 9 & 12 \end{bmatrix}$

 A+B+C =$\begin{bmatrix} 9\\12 \end{bmatrix}$   and (A+B+C)'= $\begin{bmatrix} 9 & 12 \end{bmatrix}$

C is the answer

Comments

Good explanation