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

Question

Find the value of a, b, c and d from the following equation:
$\left[\begin{array}{ll}{2 a+b} & {a-2 b} \\ {5 c-d} & {4 c+3 d}\end{array}\right]$ = $\left[\begin{array}{cc}{4} & {-3} \\ {11} & {24}\end{array}\right]$

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Answer

$\left[\begin{array}{ll}{2 a+b} & {a-2 b} \\ {5 c-d} & {4 c+3 d}\end{array}\right]$ = $\left[\begin{array}{cc}{4} & {-3} \\ {11} & {24}\end{array}\right]$
As the given matrices are equal, therefore their corresponding elements must be equal.
Comparing the corresponding elements, we get
2a + b = 4 ...(i)
a - 2b = -3 .....(ii)
5c - d = 11 ....(iii)
4c + 3d = 24 ....(iv)
Multiplying (i) by 2 and adding to (ii), we get
5a = 5 $\Rightarrow$ a = 1
$\Rightarrow$ b = 4 - 2(1) = 2
Multiplying (iii) by 3 and adding to (iv), we get
19c = 57 $\Rightarrow$ c = 3
$\Rightarrow$ d = 5(3) - 11 = 4
Hence, a = 1, b = 2, c = 3, d = 4

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