Question

Evaluate the determinant for the following matrix:

-4 -4 -3 
                                                                                 3  3 -5 
                                                                                -5  2 -5
 A. –203 B. 75 C. –152 D. –263

Answer 1

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

Answer 2

The determinant of matrix is -203

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.