M=[[5,1,3],[-3,2,6],[2,3,9]] হলে |M|= কোনটি?

Explanation:

Another Explanation (5): \( M=\begin{bmatrix} 5 & 1 & 3 \\ -3 & 2 & 6 \\ 2 & 3 & 9 \end{bmatrix} \) \( |M| \) নির্ণয় করতে হবে। \( \begin{aligned} |M| &= 5 \begin{vmatrix} 2 & 6 \\ 3 & 9 \end{vmatrix} - 1 \begin{vmatrix} -3 & 6 \\ 2 & 9 \end{vmatrix} + 3 \begin{vmatrix} -3 & 2 \\ 2 & 3 \end{vmatrix} \\ &= 5(2 \cdot 9 - 6 \cdot 3) - 1((-3) \cdot 9 - 6 \cdot 2) + 3((-3) \cdot 3 - 2 \cdot 2) \\ &= 5(18 - 18) - 1(-27 - 12) + 3(-9 - 4) \\ &= 5(0) - 1(-39) + 3(-13) \\ &= 0 + 39 - 39 \\ &= 0 \end{aligned} \) অতএব, \( |M| = 0 \) 🥳🎉