Solve this system of equations using row echelon form:
3x – 3y – 6z = -126x – 2y – 8z = -163x – 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.
Answer
(0, 0, 2)
Find reduced row echelon form of this matrix:
Try these elementary row operations: , switch R1 and R3.
Solve using reduced row echelon form:
Try these elementary row operations: R1 = R1 – 3(R3), R2 = R2 – 2(R1), R3 = R3 – R1, R3 = R3 – R2.
Infinitely many solutions.
Solve this system of equations:
3x + y – 3z = 142x + y – 2z = 11x – z = 2
Try these elementary row operations: R1 = R1 – R2, R3 = R3 – R1. Uh oh. Something went wrong here.
Our resulting matrix is:
No solution because 0 ≠ -1.
Solve for x and y:
Multiply the inverse of to
(3, 1)
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, switch R1 and R3.
to 