Solve the system using matrices (row operations) Solve the system using matrices

Question

Solve the system using matrices (row operations)

Solve the system using matrices (row operations) -2x + y - 3z = 7 x - 2y - 2z = -18 3x - 5y - 6z = -18 3x - 5y - 6z = -49 How many solutions are there to this system? None Exactly 1 Exactly 2 Exactly 3 Infinitely many None of the above If there is one solution, give its coordinates in the answer spaces below. If there are infinitely many solutions, enter z in the answer blank for z, enter a formula for y in terms of z in the answer blank for y and enter a formula for x in terms of z in the answer blank for x. If there are no solutions, leave the answer blanks for x, y and z empty. x = y = z =

Explanation / Answer

Your matrix

Find the pivot in the 1st column and swap the 2nd and the 1st rows

Eliminate the 1st column

Find the pivot in the 2nd column and swap the 3rd and the 2nd rows

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by -7

Eliminate the 3rd column

Solution

x = -4

y = 5

z = 2

X1 X2 X3 b 1 -2 1 -3 7 2 1 -2 -2 -18 3 3 -5 -6 -49

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