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Intermediate Algebra question!?
4. Solve the system of equations using matrices: please show work
1) 3x + 3y + 3z = 12
2) 2x + 2y - z = - 4
3) -x + y - z = - 2
5. Solve the system of equations using matrices (please show work):
1) -x + 4y - z = 8
2) 4x - y + 3z = 9
3) 2x + 7y + z = 0
1 Answer
- 9 years agoFavorite Answer
L1 --> [ 3 3 3 12 ]
L2 --> [ 2 2 -1 -4 ]
L3 --> [ -1 1 -1 -2 ]
L1 becomes equal to 3*(L3) + L1
[ 0 6 0 6 ]
[ 2 2 -1 -4 ]
[ -1 1 -1 -2 ]
L2 becomes equal to 2*(L3) + L2
L1 becomes equal to (1/6)*(L1)
[ 0 1 0 1 ]
[ 0 4 -3 -8 ]
[ -1 1 -1 -2 ]
L2 becomes equal to 4(L1) - L2
[ 0 1 0 1 ]
[ 0 0 3 -4 ]
[ -1 1 -1 -2 ]
L2 becomes equal to (1/3)(L2)
[ 0 1 0 1 ]
[ 0 0 1 -4/3 ]
[ -1 1 -1 -2 ]
L3 becomes equal to L1-L3
[ 0 1 0 1 ]
[ 0 0 1 -4/3 ]
[ 1 0 1 3 ]
L3 becomes equal to L2 - L3
[ 0 1 0 1 ]
[ 0 0 1 -4/3 ]
[ -1 0 0 -13/3 ]
L3 becomes equal to -(L3)
[ 0 1 0 1 ]
[ 0 0 1 -4/3 ]
[ 1 0 0 13/3 ]
Rearrange if you want to
[ 1 0 0 13/3 ]
[ 0 1 0 1 ]
[ 0 0 1 -4/3 ]
X = 13/3, Y = 1, Z = -4/3