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DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS1 Mark
MCQ
For which of the following element in the determinant $\triangle=\begin{bmatrix}5&-5&8\\6&2&-1\\5&-6&8\end{bmatrix},$ the minor and the cofactor both are zero.
  • A
    -5
  • ✓
    2
  • C
    -6
  • D
    8
✓

Answer

Correct option: B.
2
Consider the element 2 in the determinant $\triangle=\begin{bmatrix}5&-5&8\\6&2&-1\\5&-6&8\end{bmatrix}$

The minor of the element 2 is given by

$\therefore\text{M}_{22}=\begin{bmatrix}5&8\\5&8\end{bmatrix}=40-40=0$

$\Rightarrow\text{A}^{22}=(-1)^2+2 (0)=0.$

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