Find the values of a, ,b, , c, and d from the following equation:… - Vidyadip

MCQ

Find the values of $a, \,b,\, c,$ and $d$ from the following equation:

$\left[\begin{array}{cc}
2 a+b & a-2 b \\
5 c-d & 4 c+3 d
\end{array}\right]=\left[\begin{array}{cc}
4 & -3 \\
11 & 24
\end{array}\right]$

✓
$a=1$, $b=2$, $c=3$, $d=4$
B
$a=1$, $b=4$, $c=3$, $d=4$
C
$a=1$, $b=2$, $c=5$, $d=4$
D
$a=8$, $b=2$, $c=3$, $d=4$

✓

Answer

Correct option: A.

$a=1$, $b=2$, $c=3$, $d=4$

a
Solution By equality of two matrices, equating the corresponding elements, we get

$\begin{array}{ll}
2 a+b=4 & 5 c-d=11 \\
a-2 b=-3 & 4 c+3 d=24
\end{array}$

Solving these equations, we get

$a=1$, $b=2$, $c=3$ and $d=4$

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