Your given matrix can be written as:
[tex] \left[\begin{array}{ccc}2&-2&1\\1&5&-7\\1&-1&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\x\end{array}\right] = \left[\begin{array}{ccc}0\\3\\-7\end{array}\right][/tex]
which we can interpret as Ax=B
In Cramer's rule, to get the value of a variable, first we will take the determinant (A) of the original matrix. Then, we will substitute the values of B on the column representing the variable and take its determinant (A1).
You can solve for the determinant by multiplying the diagonals with a right-downward direction and add them to the diagonals to the left-downward direction. (Sorry, I can't explain it in words. If you're having troubles with that, you can consult your textbooks or the internet for further explanation.) The determinant (A) is -18.
Then, we will replace the values on the column representing the variable by B. Since I'm not good at words, I'm just gonna show you how it works.
In getting x, the matrix will be:
[tex] \left[\begin{array}{ccc}0&-2&1\\3&5&-7\\-7&-1&-1\end{array}\right] [/tex]
Did you notice that the values on the first column were replaced by the values of B? That is what I meant.
The determinant (A1) for the matrix is 54.
Therefore, we will do [tex] \frac{A1}{A} [/tex]
=[tex] \frac{54}{-18} [/tex]
=-3
Thus, x=-3.
Do this with y and z.
If you're still having trouble, don't hesitate to message me.
