Question

Evaluate the determinant of the matrix. -4 5 6 0 4 4 -2 -5 4 I need the work plz

Answer 1

Answer:

-136

Step-by-step explanation:

We have to find the determinant of the following matrix:

$\left[\begin{array}{ccc}-4&5&6\\0&4&4\\-2&-5&4\end{array}\right]$

We can find the determinant by expanding via 1st column. i.e. by taking each element of 1st column and multiplying it by its co-factor matrix as shown below:

det $\left[\begin{array}{ccc}-4&5&6\\0&4&4\\-2&-5&4\end{array}\right]$

= $(-4 \times det \left[\begin{array}{cc}4&4\\-5&4\end{array}\right]) - (0 \times (-4 \times det \left[\begin{array}{cc}5&6\\-5&4\end{array}\right]))+ ((-2) \times det\left[\begin{array}{cc}5&6\\4&4\end{array}\right])\\\\ =-4 \times (16 + 20)-(0)+(-2 \times 20-24)\\\\ =-4(36)+(-2(-4))\\\\ =-144+8\\\\ =-136$

The notation det() stands for determinant of the matrix.

Therefore, the determinant of the given matrix is -136