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DETERMINANTS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDETERMINANTS1 Mark
MCQ
Evaluate $\begin{bmatrix}8\text{x}+1&2\text{x}-2\\\text{x}^2-1&3\text{x}+5\end{bmatrix}$ is:
  • A
    $-2x^{3 }- 26x^{2 }+ 45x + 3$
  • ✓
    $-2x^{3 }+ 26x^{2 }+ 45x + 3$
  • C
    $-2x^{3 }+ 26x^{2 }+ 45x - 3$
  • D
    $-2x^{3 }- 26x^2- 45x + 3$
✓

Answer

Correct option: B.
$-2x^{3 }+ 26x^{2 }+ 45x + 3$

Expanding along the first row, we get
$\triangle=8\text{x}+1(3\text{x}+5)-(2\text{x}-2)(\text{x}^2-1)$
$=(24\text{x}^2+43\text{x}+5)-(2\text{x}^3-2\text{x}^2-2\text{x}+2)$
$=-2\text{x}^3+26\text{x}^2+45\text{x}+3.$

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