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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices2 Marks
Question
Let $M \times\left[\begin{array}{ll}1 & 1 \\ 0 & 2\end{array}\right]=\left[\begin{array}{ll}1 & 2\end{array}\right]$ where $M$ is a matrix.
(i) State the order of matrix M
(ii) Find the matrix $M$
✓

Answer

Given
(i) $M$ is the order of $1 \times 2$
$
\begin{aligned}
& \text { let } M=[ x y] \\
& \therefore\left[\begin{array}{ll}
x & y
\end{array}\right] \times\left[\begin{array}{ll}
1 & 1 \\
0 & 2
\end{array}\right]=\left[\begin{array}{ll}
1 & 2
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{ll}
x+0 & x+2 y
\end{array}\right]=\left[\begin{array}{ll}
1 & 2
\end{array}\right]
\end{aligned}
$
Comparing the corresponding elements
$
\begin{aligned}
& x=1 \text { and } x+2 y=2 \\
& \Rightarrow 1+2 y=2 \\
& \Rightarrow 2 y=2-1=1 \\
& \Rightarrow y=\frac{1}{2}
\end{aligned}
$
Hence $x=1, y=\frac{1}{2}$
$
\therefore M=\left[\begin{array}{ll}
1 & \frac{1}{2}
\end{array}\right] .
$

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