Question

can u pls help me solve the following equation using cramer's rule 3x + 4y + 2z = 3; 2x - 3y - z = -3; x + 2y + z = 4

Answer 1

when using cramer's rule, You must have a matrix of the system, that is A = \[\left[\begin{matrix}3 & 4&2 \\ 2 & -3&1\\1&2&1\end{matrix}\right]\] and the solution is \[\left(\begin{matrix}3 \\ -3\\4\end{matrix}\right)\]
You replace the solution into the column of A. Correspondingly, the first column is x, then y, then z
so, you replace the solution matrix (which is 3 x1 matrix ) into the first column, you have another matrix called A_1 that is \[\left[\begin{matrix}3 & -3&4 \\ 4 & -3&2\\2&1&1\end{matrix}\right]\]
from now on, you can calculate x by cramer's rule. that is \[x = \frac{ \det (A1)}{ \det (A) }\]
you know how to calculate those dets, right?
repeat the same step to get y, then get z
You should practice to get experience when applying cramer's rule. It is not all of matrices can solve by using the very easy rule like that. Having a matrix can be solved by cramer's rule is a grant