Use Gauss-Jordan elimination to solve the linear system. If the system has infin

Question

Use Gauss-Jordan elimination to solve the linear system. If the system has infinitely many solutions , describe the solution as an ordered triple involving a free variable. -x+ y+ z= -4 -x+4y-14z= -25 7x-3y-27z= 0

Explanation / Answer

Turning it into a matrix: [-1 1 1 -3] [-1 3 -7 -13] [5 -2 -17 0] => [1 -1 -1 3] [-1 3 -7 -13] [5 -2 -17 0] => [1 -1 -1 3] [0 2 -8 -10] [5 -2 -17 0] => [1 -1 -1 3] [0 1 -4 -5] [0 3 -12 -15] => [1 0 -5 8] [0 1 -4 -5] [0 1 -4 -5] => [1 0 -5 8] [0 1 -4 -5] [0 0 0 0] So x - 5z = 8 and y - 4z = -5 => x = 5z + 8 and y = 4z - 5. So there are infinitely many solutions and they are of the form (5z+8, 4z-5, z) for some free variable z

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