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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices1 Mark
MCQ
If $2\left[\begin{array}{ll}3 & 4 \\ 5 & x\end{array}\right]+\left[\begin{array}{ll}1 & y \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}7 & 0 \\ 10 & 5\end{array}\right]$, then the values of $x$ and $y$ are:
  • A
    $x=4, y=-4$
  • ✓
    $x=2, y=-8$
  • C
    $x=2, y=-4$
  • D
    $x=4, y=-8$
✓

Answer

Correct option: B.
$x=2, y=-8$
(b) $x=2, y=-8$
Explanation:
$\begin{array}{l}2\left[\begin{array}{ll}3 & 4 \\ 5 & x\end{array}\right]+\left[\begin{array}{ll}1 & y \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}7 & 0 \\ 10 & 5\end{array}\right] \\ \Rightarrow\left[\begin{array}{cc}6 & 8 \\ 10 & 2 x\end{array}\right]+\left[\begin{array}{ll}1 & y \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}7 & 0 \\ 10 & 5\end{array}\right] \\ \Rightarrow\left[\begin{array}{cc}7 & 8+y \\ 10 & 2 x+1\end{array}\right]=\left[\begin{array}{cc}7 & 0 \\ 10 & 5\end{array}\right] \\ \Rightarrow 8+y=0\end{array}$
and $2 x+1=5$
$\begin{array}{l}\Rightarrow y=-8 \\ \text { and } x=2 .\end{array}$

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