Question

What is the solution of the system of equations? (1 point)

(5, –2, 7)
(–5, 2, 7)
(5, 2, –7)
no solution

What is element a_23 in matrix A? (1 point)
–5
3
–4
8

Answer 1

Part (a)
The system of equations may be written in matrix form, as
[A]{x} = {B}
where

`[A] = \left[\begin{array}{ccc}-3&-4&-3\\2&-6&2\\5&-2&5\end{array}\right] , \,\, {x}= \begin{bmatrix}x\\y\\z \end{bmatrix} , \,\, {B} = \begin{bmatrix} -7\\3\\9\end {bmatrix}`

In order for the system of equations to have a solution,

`det[A] \\e 0`

Evaluate det[A].
det[A] = -3(-30 + 4) + 4(10 - 10) - 3(-4 + 30) = 0
Because det[A] = 0, there is no solution.

Answer: No solution

Part (b)
The given matrix is

`A = \begin{bmatrix} 8&-4&-3\\3&-9&-5\\-8&8&8\end{bmatrix}`
The element a₂₃ is -5.

Answer: -5