Question

Evaluate the determinant for the following matrix:

Answer 1

Answer:

The determinant of matrix is -203            

Step-by-step explanation:

Given the matrix of order 3 i.e

$A=\begin{bmatrix}-4&-4&-3\\ 3&3&-5\\ -5&2&-5 \end{bmatrix}$

we have to find the determinant of matrix A

$|A|=-4(-5(3)-(-5)(2))-3((-4)(-5)-(-3)(2))+(-5)((-5)(-4)-(-3)(3))\\\\|A|=-4(-15+10)-3(20+6)-5(20+9)\\\\|A|=-4(-5)-3(26)-5(29)\\\\|A|=20-78-145\\\\|A|=-203$

Hence, the determinant of matrix is -203

Option A is correct.

Answer 2

Looks like it is from China, but... I color coded the numbers. Multiply across the dashed lines.