Question

Help please

Answer 1

Hi, I need help with this problem. I don't understand it.

Answer 2

Okay this is just based on targeted guessing but if you see the above matrix, the pattern is [coefficient of x, R.H.S, coefficient of z]. Since y is the only thing omitted, I think y

Answer 3

That is the Crammer's rule to find x,y, z

Answer 4

When applying it, you need know the determinant of the system.
Like this:
The original one is \(A \vec x=b\), and your A is
\(A=\left [\begin{matrix}1&2&-1\\2&3&2\\1&-2&-2\end{matrix}\right]\)

Let the first column is \(A_1\)
the second column is \(A_2\) and the third one is \(A_3\)
then, your A is \(A = \left[A_1~~A_2~~A_3\right]\)
ok?

Answer 5

On the original one, your b is \(\vec b= \left[\begin{matrix}-7\\-3\\3\end{matrix}\right]\)

Answer 6

The Crammer's rule says that to find x, you do:
replace \(A_1\) by \(\vec b\) to get a new matrix, say \(A_x\), then \(x=\dfrac{det A_x}{det A}\)

Answer 7

to find y, you do the same, but replace \(A_2 \) by \(\vec b\) to get a new matrix, say \(A_y\)
then \(y =\dfrac{det A_y}{det A}\), that is what you show on the question

Answer 8

got what I meant?

Answer 9

Same method to find z
You have \(A\vec x=b\) and then \(\vec x = A^{-1}b\)
However, not all A is invertible, Crammer's rule allow you to find \(\vec x\) if A is not invertible.