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DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS1 Mark
MCQ
Choose the correct answer from given four options in each of the Exercise: There are two values of a which makes determinant $\begin{bmatrix}1 & -2 & 5 \\2 & \text{a} & 1\\0 & 4 & 2\text{a} \end{bmatrix} = 86,$ then sum of these number is:
  • A
    $4$
  • B
    $5$
  • ✓
    $-4$
  • D
    $9$
✓

Answer

Correct option: C.
$-4$
We have,
$\begin{bmatrix}1 & -2 & 5 \\2 & \text{a} & 1\\0 & 4 & 2\text{a} \end{bmatrix} = 86,$
$\Rightarrow\ 1(2\text{a}^{2} + 4) - 2(-4\text{a} - 20) + 0 = 86 [$Expanding along $C_1]$
$\Rightarrow\ \text{a}^{2} + 4\text{a} - 21 = 0$
$\Rightarrow\ \text{(a + 7)} (\text{a} - 3) = 0$
$\Rightarrow\ \text{a} = -7 $ and $ 3$
$\therefore$ Required sum $= -7 + 3 = -4$

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