Question

Determine the cofactor of a13 the matrix. A=[ matrix 2&-4&0\\ 6&5&7\\ 5&2&0 matrix ]

Answer 1

-168

Explanation:

`\left[\begin{array}{ccc}2&-4&0\\6&5&7\\5&2&0\end{array}\right]`

determinant can be found by cofactor expansion:

say along third column:

`a_(13) \det(\left[\begin{array}{cc}6&5\\5&2\end{array}\right] ) -a_(23) \det \ (\left[\begin{array}{cc}2&-4\\5&2\end{array}\right] ) +a_(33) \det(\left[\begin{array}{cc}2&-4\\6&5\end{array}\right] )`

`=0 -(7)[(2)(2)-(-4)(5)] +0`

`=-168`