`x + 2y - 3z = -28, 4y + 2z = 0, -x + y - z = -5` Use matricies to solve the system of equations. Use Gaussian elimination with back-substitution.

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The equations in the matrix form can be written as,


Add Row 1 and Row 3


Multiply Row 2 by 2 and Add it to Row 3 


Now the equations can be written as,

`x+2y-3z=-28`     ----- equation 1

`4y+2z=0`            ------ equation 2

`11y=-33`               ----- equation 3

From equation 3,


Substitute back y in equation 2,





substitute back y and z in equation 1,





So the solutions are x=-4, y=-3, z=6

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