Question

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

Answer 1

Answer:

$A' = -51$

Step-by-step 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