Systems of Equations

Michigan State University - Diagnostic Exam

Find the value of z in the solution of the system.

$x + 2y - z = 0 x - z = 2 2x + y = 3$

a) -1 b) 0 c) 1 d) 2 e) 3

Solution:

Let $( ) 1 2 - 1 || || | 1 0 - 1 | A= || || |( 2 1 0 |)$ and $( ) 1 2 0 || || | 1 0 2 | C = || || |( 2 1 3 |)$ .

Then by Cramer’s rule $|C-|- -0- z = |A | = - 4 = 0$

Diagnostic:

If you miss this question please review linear systems with 3 variables.

July 15, 2008