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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices4 Marks
Question
In the given case below find
$(a)$ The order of matrix $M$.
$(b)$ The matrix $M$
$M \times\left[\begin{array}{ll}1 & 1 \\ 0 & 2\end{array}\right]=[1,2]$
✓

Answer

We know, the product of two matrices is defined only when the number of columns of the first matrix is equal to the number of rows of the second matrix
Let the order of matrix $M$ be $a \times b.$
$M_{a \times b} \times\left[\begin{array}{ll}1 & 1 \\ 0 & 2\end{array}\right]_{2 \times 2}=\left[\begin{array}{ll}1 & 2\end{array}\right]_{1 \times 2}$
Clearly, the order of matrix $M$ is $1 \times 2$
Let $M=[a, b]$
$\begin{array}{l}M \times\left[\begin{array}{ll}1 & 1 \\ 0 & 2\end{array}\right]=\left[\begin{array}{ll}1 & 2\end{array}\right] \\ {[a, b] \times\left[\begin{array}{ll}1 & 1 \\ 0 & 2\end{array}\right]=\left[\begin{array}{ll}1 & 2\end{array}\right]} \\ {[a+0 \quad a+2 b]=[1,2]}\end{array}$
Comparing the corresponding elements we get
$a=1 $ and $ a+2 b=2$
$ \Rightarrow 2 b=2-1=1 $
$\Rightarrow b=\frac{1}{2}$
$\therefore M=\left[a b\right]=\left[1 \frac{1}{2}\right]$

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