Question

What is the determinant?

(3x3 Matrix)

[ -2 2 b
0 3 a
0 0 -5]

Answer 1

Look at the picture.

`A= \left[\begin{array}{ccc}-2&2&b\\0&3&a\\0&0&-5\end{array}\right]`


`\boxed{\det A=30}`

Answer 2

Use the rule:

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

`=a\cdot e\cdot i+d\cdot h\cdot c+b\cdot f\cdot g-c\cdot e\cdot g-f\cdot h\cdot a- b\cdot d\cdot i`.
Then,

`\left| \left[\begin{array}{ccc}-2&2&b\\0&3&a\\0&0&-5\end{array}\right] \right|=`

`=-2\cdot 3\cdot (-5)+2\cdot a\cdot 0+0\cdot 0\cdot b-b\cdot 3\cdot 0-a\cdot 0\cdot (-2)- 0\cdot 2\cdot (-5)=30`.
Answer: 30