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Questions  >>  CBSE XII  >>  Math  >>  Matrices
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Q)

$A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}\;and\;B=\begin{bmatrix}4 & 0\\1 & 3\\2 & 6\end{bmatrix},then\;verify \;that:(iii)\quad(KA)'=(KA')$

Note: This is part 3 of a 3 part question, split as 3 separate questions here.

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A)
Toolbox:
  • If A_{i,j} be a matrix m*n matrix , then the matrix obtained by interchanging the rows and column of A is called as transpose of A.
Step1:
(iii)Given:-
$A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}$
LHS:-
$KA=K\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}$
$(KA)=\begin{bmatrix}0 &-K&2K\\4K & 3K&-4K\end{bmatrix}$
$(KA)'=\begin{bmatrix}0 &4K\\-K&3K \\ 2K&-4K\end{bmatrix}$
Step2:
RHS:-
$A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}$
$A'=\begin{bmatrix}0 & 4 \\-1 & 3 \\2& -4\end{bmatrix}$
$(KA')=K\begin{bmatrix}0 & 4 \\-1 & 3 \\2& -4\end{bmatrix}$
$\;\;\;=\begin{bmatrix}0 & 4K \\-K & 3K \\2K& -4K\end{bmatrix}$
$\Rightarrow LHS=RHS.$
$\Rightarrow (KA)'=(KA')$
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