Part (a)
The system of equations may be written in matrix form, as
[A]{x} = {B}
where
[tex][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}[/tex]
In order for the system of equations to have a solution,
[tex]det[A] \ne 0[/tex]
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
[tex]A = \begin{bmatrix} 8&-4&-3\\3&-9&-5\\-8&8&8\end{bmatrix}[/tex]
The element a₂₃ is -5.
Answer: -5
