Question

What is the determinant of A={-2 2 -5
{4 -1 -2 }
{ 1 3 -5

Answer 1

`A' = -51`

Explanation:

Given

`A = \left[\begin{array}{ccc}-2&2&-5\\4&-1&-2\\1&3&-5\end{array}\right]`

Required

Determine the determinant of A (A')

If

`A = \left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right]`

Then,

`A' = a(e*i - f * h) - b(d * i - g * f) + c(d * h - e * g)`

So:

The determinant of
`A = \left[\begin{array}{ccc}-2&2&-5\\4&-1&-2\\1&3&-5\end{array}\right]` is

`A' = -2(-1 * -5 -(-2)*3) -2(4 * -5 -(-2) * 1) -5(4 * 3- (-1) * 1)`

`A' = -2(5 +6) -2(-20 +2) -5(12 + 1)`

`A' = -2(11) -2(-18) -5(13)`

`A' = -22 +36 -65`

`A' = -51`

Hence, the determinant is -51