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Determinants and Matrices — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDeterminants and Matrices2 Marks
Question
$
{If }\left[\begin{array}{cc}
2 x+1 & -1 \\
3 & 4 y
\end{array}\right]+\left[\begin{array}{cc}
-1 & 6 \\
3 & 0
\end{array}\right]=\left[\begin{array}{cc}
4 & 5 \\
6 & 12
\end{array}\right] \text {, }
$
find $x$ and $y$.
✓

Answer

$
\begin{aligned}
& \text { Given } {\left[\begin{array}{cc}
2 x+1 & -1 \\
3 & 4 y
\end{array}\right]+\left[\begin{array}{cc}
-1 & 6 \\
3 & 0
\end{array}\right] } \\
&=\left[\begin{array}{cc}
4 & 5 \\
6 & 12
\end{array}\right] \\
& \therefore\left[\begin{array}{cc}
2 x & 5 \\
6 & 4 y
\end{array}\right]=\left[\begin{array}{cc}
4 & 5 \\
6 & 12
\end{array}\right]
\end{aligned}
$
$\therefore$ Using definition of equality of matrices, we have
$
2 x=4, \quad 4 y=12 \quad \therefore x=2, \quad y=3
$

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