Question

The value of the cofactor of the element of second row and third column in the matrix \[ \begin{bmatrix} 4 & 3 & 2 \\ 2 & -1 & 0 \\ 1 & 2 & 3 \end{bmatrix} \text{ is:} \]

• A. 5
• B. -5
• C. -11
• D. 11

Hint:

Cofactor = $(-1)^{i+j} \times$ Minor.

Answer 1

The Correct Option is A

Element is in 2nd row, 3rd column: element = 0. But cofactor depends on minor: Remove 2nd row and 3rd column: \[ \text{Minor} = \begin{vmatrix} 4 & 3 \\ 1 & 2 \end{vmatrix} = (4)(2) - (3)(1) = 8 - 3 = 5. \] Cofactor = $(-1)^{2+3} \times$ Minor = $(-1)^5 \times 5 = -5$. So the answer is (B) -5. %Quciktip