Question

solve using matrices and row-reduction. if there is no solution, indicate why. if there are an infinite number so solutions, give the general form of the solution.

x + 2y + z = 6
2x + y - 4z = 3
x + 3 y + 3z = 9

Answer 1

The determinant of the matrix of coefficients=

1(3+12)-2(6+4)+1(6-1)=15-20+5=0. This means we can't use matrices for solving, and there is inconsistency or many solutions.

A. x+2y=6-z,

B. 2x+y=3+4z,

C. x+3y=9-3z.

2B-A: 3x=9z, x=3z; 2y=6-z-x=6-4z, y=3-2z.

Substitute for x and y in C: 3z+9-6z=9-3z, so we have 9-3z=9-3z which cannot determine z, so there are many solutions for x and y, dependent on z, which can take any value.