Question 232022
There are many ways to use matrices to solve systems of equations like this. I'll use the one that is often the first one taught:
{{{(matrix(3, 4,
1, 3, -4, 13,
2, 7, -3, 11,
-2, -1, 2, -8)
)
}}}
Add -2*Row 1 to the second row and 2*row 1 to the third row:
{{{(matrix(3, 4,
1, 3, -4, 13,
0, 1, 5, -15,
0, 5, -6, 18))}}}
Add -3*Row 2 to the first row and -5*Row 2 to the third row:
{{{(matrix(3, 4,
1, 0, -19, 58,
0, 1, 5, -15,
0, 0, -31, 93))}}}
Multiply Row 3 by -1/31:
{{{(matrix(3, 4,
1, 0, -19, 58,
0, 1, 5, -15,
0, 0, 1, -3))}}}
Add 19*Row 3 to row 1 and add -5*Row 3 to the second row:
{{{(matrix(3, 4,
1, 0, 0, 1,
0, 1, 0, 0,
0, 0, 1, -3))}}}
Solution: (1, 0, -3)