[1 Mark Question Answer]

Question 11 Mark

Find $x$ and $y,$ if $\left[\begin{array}{cc}-3 & 2 \\ 0 & -5\end{array}\right]\left[\begin{array}{l}x \\ 2\end{array}\right] =\left[\begin{array}{c}-5 \\ y\end{array}\right]$

Answer

$\left[\begin{array}{c}-3 x+4 \\ -10\end{array}\right]$
$=\left[\begin{array}{c}-5 \\ y\end{array}\right]$
$=-3 x+4$
$=-5 ;$
$y=-10 , x=3 , y=-10 .$

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Question 21 Mark

If $A = \left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right]$ and $B = \left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right]$ find $BA$.

Answer

$\begin{array}{l} BA =\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right]\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right] \end{array}$
$=\left[\begin{array}{cc}1.2+33 & 1.4+3.2 \\ -2.2+5.3 & -2.4+5.2\end{array}\right] $
$BA =\left[\begin{array}{cc}11 & 10 \\ 11 & 2\end{array}\right] .$

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Question 31 Mark

If $A=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right]$ find $AB.$

Answer

$\begin{array}{l} AB =\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right]\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right]\end{array} $
$=\left[\begin{array}{ll}2.1+4 \cdot(-2) & 2.3+4.5 \\ 3.1+2 \cdot(-2) & 3.3+2.5\end{array}\right]$
$AB =\left[\begin{array}{ll}-6 & 26 \\ -1 & 19\end{array}\right]$

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Question 41 Mark

Find $x$ and $y,$ if $\left(\begin{array}{ll}x & 3 x \\ y & 4 y\end{array}\right)\left(\begin{array}{l}2 \\ 1\end{array}\right)=\left(\begin{array}{c}5 \\ 12\end{array}\right)$.

Answer

On multiplying $\text{L.H.S.},$ matrices,
we get $\left(\begin{array}{l}5 x \\ 6 y\end{array}\right)$
which is equal to $\text{R.H.S.},$ matrix, evaluate their corresponding elements to get the values of $x$ and $y$.
Hence$, x = 1, y = 2.$

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Question 51 Mark

Given$\left[\begin{array}{cc}2 & 1 \\ -3 & 4\end{array}\right] X =\left[\begin{array}{l}7 \\ 6\end{array}\right]$. the order of the matrix $X.$

Answer

$\left[\begin{array}{cc}2 & 1 \\ -3 & 4\end{array}\right] X=\left[\begin{array}{l}7 \\ 6\end{array}\right]$
The order of matrix $X = 2 \times 1.$

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