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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices2 Marks
Question
Find the values of $\mathrm{a}, \mathrm{b}, \mathrm{c}$ and $\mathrm{d}$ from the equation $\left[\begin{array}{cc}a-b & 2 a+c \\ 2 a-b & 3 c+d\end{array}\right]=\left[\begin{array}{cc}-1 & 5 \\ 0 & 13\end{array}\right]$.
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Answer

Equating corresponding entries,
a - b = -1 ……….(i)
2a - b = 0 ……….(ii)
2a + c = 5 ……….(iii)
3c + d = 13 ……….(iv)
Eq. (i) – Eq. (ii) = -a = -1
$\Rightarrow$ a = 1
Putting a = 1 in eq. (i), 1 - b = -1
$\Rightarrow$ -b = -2 $\Rightarrow$ b = 2
Putting a = 1 in eq. (iii), 2 + c = 5
$\Rightarrow$ c = 5 - 2 $\Rightarrow$ c = 3
Putting c = 3 in eq. (iv), 9 + d = 13
$\Rightarrow$ d = 13 - 9 $\Rightarrow$ d = 4
$\Rightarrow$ a = 1, b = 2, c = 3, d = 4

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