# Math Help - Matrix methods- using row operations

1. ## Matrix methods- using row operations

1.) 7x + 5y - z = 94
x + 5y + 2z = 52
2x + y + z = 29

THANK YOU!

2. You want to know the value of the determinant or solve the variables?

The determinant is simply (by the last row):

$|A| = 2(5 * 2-5(-1)) - (7 * 2-1(-1)) + (7*5-1 *5) = 45$

(How do I type the multiplication sign?)

You can solve the variables by using the Cramer rule, i.e., by replacing each of the columns one by one by the exogenous variables vector and solving the determinant and then $|A_1| / |A|$