Question

If A=\(\begin{bmatrix}2&5&9\\6&1&3\\4&8&2\end{bmatrix}\), find |A|.

(a) 352

(b) 356

(c) 325

(d) 532

I got this question by my school teacher while I was bunking the class.

My doubt stems from Determinant topic in division Determinants of Mathematics – Class 12

Answer 1

Right answer is (a) 352

To explain: Given that, A=\(\begin{bmatrix}2&5&9\\6&1&3\\4&8&2\end{bmatrix}\)

⇒|A|=\(\begin{vmatrix}2&5&9\\6&1&3\\4&8&2\end{vmatrix}\)

Evaluating along the first row, we get

∆=2\(\begin{vmatrix}1&3\\8&2\end{vmatrix}\)-5\(\begin{vmatrix}6&3\\4&2\end{vmatrix}\)+9\(\begin{vmatrix}6&1\\4&8\end{vmatrix}\)

∆=2(2-24)-5(12-12)+9(48-4)

∆=2(-22)-0+9(44)

∆=-44+9(44)=44(-1+9)=352