Systems of Equations Exercises

Solve this system of equations using row echelon form:

3x – 3y – 6z = -12
6x – 2y – 8z = -16
3x – y – 3z = -6

Hint

Put in augmented matrix form, and try the following elementary row operations: R2 = -2(R1) + R2, R3 = R3 – R1, R3 = 2(R3) – R2, R1/3, R2/4, R3/2.

Find reduced row echelon form of this matrix:

Hint

Try these elementary row operations: , switch R1 and R3.

Solve using reduced row echelon form:

Hint

Try these elementary row operations: R1 = R1 – 3(R3), R2 = R2 – 2(R1), R3 = R3 – R1, R3 = R3 – R2.

Solve this system of equations:

3x + y – 3z = 14
2x + y – 2z = 11
x – z = 2

Hint

Try these elementary row operations: R1 = R1 – R2, R3 = R3 – R1. Uh oh. Something went wrong here.

Solve for x and y:

Hint

Multiply the inverse of to