Question

Calculate the value of the following determinants: | 1 -1 3 2 5 0 -3 1 2 | and | -1 -8 2 9 1 0 4 1 2 |

Answer 1

Answer:

1) The determinant = 65

2) The determinant = 152

Step-by-step explanation:

Let us show how to find the determinant of a matrix

You can find the determinant of this Matrix  $\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&m&n\end{array}\right]$

by using this rule

Determinant = a(en - fm) - b(dn - fg) + c(dm - eg)

Let us use this rule with the given matrices

1)

 $\left[\begin{array}{ccc}1&-1&3\\2&5&0\\-3&1&2\end{array}\right]$

The determinand = 1[(5)(2) - (0)(1)] - (-1)[(2)(2) - (0)(-3)] + 3[(2)(1) - 5(-3)]

= 1[10 - 0] - (-1)[4 - 0] + 3[2 - (-15)]

= 1[10] + 1[4] + 3[2+15]

= 10 + 4 + 3[17]

= 10 + 4 + 51

= 65

The determinant = 65

Let us do the second one

2)

 $\left[\begin{array}{ccc}-1&-8&2\\9&1&0\\4&1&2\end{array}\right]$

The determinand = -1[(1)(2) - (0)(1)] - (-8)[(9)(2) - (0)(4)] + 2[(9)(1) - 1(4)]

= -1[2 - 0] - (-8)[18 - 0] + 2[9 - 4]

= -1[2] + 8[18] + 2[5]

= -2 + 144 + 10

= 152

The determinant = 152