Question

Reduce the matrix
[1,2,-1;-1,3,3;0,2,-1]
to echelon form​

Answer 1

[1, 0, 0; 0, 1, 0; 0, 0, 1]

Explanation:

[1, 2, -1; -1, 3, 3; 0, 2, -1]

Row Operation 1: Add 1 times the 1st row to the 2nd row:

[1,2,-1;0,5,2;0,2,-1]

Row Operation 2: Multiply the 2nd row by 1/5:

[1,2,-1;0,1,2/5;0,2,-1]

Row Operation 3: Add -2 times the 2nd row to the 3rd row:

[1,2,-1;0,1,2/5; 0, 0, -9/5]

Row Operation 4: Multiply the 3rd row by -5/9:

[1,2,-1;0,1,2/5; 0, 0, 1]

Row Operation 5: Add -2/5 times the 3rd row to the 2nd row:

[1,2,-1;0,1,0;0,0,1]

Row Operation 6: Add 1 times the 3rd row to the 1st row:

[1,2,0;0,1,0;0,0,1]

Row Operation 7: Add -2 times the 2nd row to the 1st row:

[1,0,0; 0,1,0;0,0,1]