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ISRO2009-62

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

  1. a null matrix
  2. $\text{A + B + C}$
  3. $\text{(A + B + C)}'$
  4. $\text{-(A + B + C})$
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Here A' is the Transpose Matrix also written At , Atr , tA  ,At  .

We knows Transpose respect addition

A' + B' + C' =( A + B + C)'  

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

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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

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