what is the answer to 2x-y-2z=1, 4x+y-z=5, x+y+4z=-5 using matrices
how to solve this math problem using matrices?
2 -1 -2 │ 1
4 1 -1 │ 5
1 1 4 │ -5
Multiply line 2 by 2.
2 -1 -2 │ 1
8 2 -2 │ 10
1 1 4 │ -5
Subtract line 2 from line 1, replace line 1.
-6 -3 0 │ -9
8 2 -2 │ 10
1 1 4 │ -5
Multiply line 2 by 2.
-6 -3 0 │ -9
16 4 -4 │ 20
1 1 4 │ -5
Add line 3 to line 2, replace line 2.
-6 -3 0 │ -9
17 5 0 │ 15
1 1 4 │ -5
Multiply line 3 by 6.
-6 -3 0 │ -9
17 5 0 │ 15
6 6 24 │ -30
Add line 1 to line 3, replace line 3.
-6 -3 0 │ -9
17 5 0 │ 15
0 3 24 │ -39
Multiply line 1 by 5; multiply line 2 by 3.
-30 -15 0 │ -45
51 15 0 │ 45
0 3 24 │ -39
Add line 2 to line 1, replace line 1.
21 0 0 │ 0
51 15 0 │ 45
0 3 24 │ -39
Divide line 1 by 21.
1 0 0 │ 0
51 15 0 │ 45
0 3 24 │ -39
Multiply line 1 by 51.
51 0 0 │ 0
51 15 0 │ 45
0 3 24 │ -39
Subtract line 1 from line 2, replace line 2.
51 0 0 │ 0
0 15 0 │ 45
0 3 24 │ -39
Divide line 2 by 5.
51 0 0 │ 0
0 3 0 │ 9
0 3 24 │ -39
Subtract line 2 from line 3, replace line 3.
51 0 0 │ 0
0 3 0 │ 9
0 0 24 │ -48
Three-in-one: divide line 1 by 51, divide line 2 by 3,
divide line 3 by 24.
1 0 0 │ 0
0 1 0 │ 3
0 0 1 │ -2
This shows that x = 0, y = 3, z = -2