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DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS1 Mark
Question
Find the value of a if $\begin{bmatrix} \text{a} - \text{b}& 2\text{a} + \text{c}\\ 2\text{a} - \text{b} & 3\text{c} + \text{d} \\ \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ 0 &13 \\ \end{bmatrix}$
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Answer

Given: $\begin{bmatrix} \text{a} - \text{b}& 2\text{a} + \text{c}\\ 2\text{a} - \text{b} & 3\text{c} + \text{d} \\ \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ 0 &13 \\ \end{bmatrix}$
$\Rightarrow\text{a} - \text{b} = - 1 $ - - - - - (1)
2a + c = 5 - - - - - -(2)
2a – b = 0 - - - - - - -(3)
3c + d =13 - - - - - - - (4)
$\text{ From (iii)} 2\text{ a } = \text{b}\Rightarrow\text{a} = \frac{\text{b}}{2}$
Putting in (i) we get $\frac{\text{b}}{2} - \text{b} = -1$
$\Rightarrow\frac{\text{b}}{2} = 1 \Rightarrow\text{b} = 2 $
$\therefore\text{a} = 1 $
(ii) $\Rightarrow$c =5 - 2 x 1 =5 - 2 = 3
(iv) $\Rightarrow$d =13 – 3 x (3) =13 - 9 = 4
i.e. a = 1, b = 2, c = 3, d = 4.

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