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

If $X=\begin{bmatrix}3 & 1 & 1\\5 & 2 & 3\end{bmatrix}$ and $Y=\begin{bmatrix}2 & 1 & 1\\7 & 2 & 4\end{bmatrix}$, find $2X-3Y$

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A)
Toolbox:
  • The sum / difference $A(+/-)B$ of two $m$-by-$n$ matrices $A$ and $B$ is calculated entrywise: $(A (+/-) B)_{i,j} = A_{i,j} +/- B_{i,j}$ where 1 ≤ i ≤ m and 1 ≤ j ≤ n.
(ii)$2X-3Y$
Given
$X=\begin{bmatrix}3 & 1 & 1\\5 & 2 & 3\end{bmatrix}$
$Y=\begin{bmatrix}2 & 1 & 1\\7 & 2 & 4\end{bmatrix}$
Replace the value of X and Y in the below equation.
$2X-3Y=2\begin{bmatrix}3 & 1 & 1\\5 & 2 & 3\end{bmatrix}-3\begin{bmatrix}2 & 1 & 1\\7 & 2 & 4\end{bmatrix}$
$\;\;\;\quad=\begin{bmatrix}6 & 2& 2\\10 & 4 & 6\end{bmatrix}+(-1)\begin{bmatrix}6 & 3 & 3\\21 & 6 & 12\end{bmatrix}$
$\;\;\;\quad=\begin{bmatrix}6 & 2& 2\\10 & 4 & 6\end{bmatrix}+\begin{bmatrix}-6 & -3 & -3\\-21 &- 6 & -12\end{bmatrix}$
$\;\;\;\quad=\begin{bmatrix}6-6 & 2-3& 2-3\\10-21 & 4-6 & 6-12\end{bmatrix}$
$\;\;\;\quad=\begin{bmatrix}0 & -1& -1\\-11 & -2 & -6\end{bmatrix}$

 

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