Cramer's Rule and Linear Systems — Engineering Board Exam Practice Questions

8 free engineering board exam reviewer questions on Cramer's Rule and Linear Systems (Advanced Engineering Mathematics), each with the correct answer and a worked solution.

1. For what value of k does the system x+y+z=3, x+2y+3z=6, x+3y+kz=10 have no solution?
2. In a two-loop circuit the mesh equations are 6I1-2I2=10 and -2I1+5I2=0 (volts, amperes). Find I1.
3. Solve 2x+y+z=9, x-y+2z=6, x+3y-z=4 and find x+y+z.
4. For what value of k does x+2y=0, 3x+ky=0 have nontrivial solutions?
5. Use Cramer's rule to find z in the system x+y+z=6, 2x-y+z=3, x+2y-z=2.
6. How many solutions does the system x+y=2, 2x+2y=5 have?
7. In Cramer's rule, the denominator D in x=Dx/D is
8. Use Cramer's rule to find x if 2x+3y=8 and x-y=-1.