Engineering Board Exam Reviewer · Cramer's Rule and Linear Systems · medium

Use Cramer's rule to find z in the system x+y+z=6, 2x-y+z=3, x+2y-z=2.

1. 2
2. 6
3. 3
4. 21

Answer

C. 3

Solution

D= vmatrix1&1&1\2&-1&1\1&2&-1 vmatrix=7 and Dz= vmatrix1&1&6\2&-1&3\1&2&2 vmatrix=21. So z=21/7=3.

More Cramer's Rule and Linear Systems questions

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

All Cramer's Rule and Linear Systems questions