Use matrices to solve system of eq (if possible). Use Gauss elimination w/ back-substitution. (If no solution, enter NO SOLUTION. If system is dependent, set w = a & solve for x, y & z in terms of a.)

Question

x-4y+3z-2w= 16

3x-2y+z-4w= -10

-4x+3y-2z+w= -5

-2x+y-4z+3w= -19

(x, y, z, w) = (______)

Answer 1

1 -4 3 -2 16

3 -2 1 -4 -10

-4 3 -2 1 -5

-2 1 -4 3 -19

-3 * row1 + row2;

4 * row1 + row3;

2 * row1 + row4;

-------------------------

1 -4 3 -2 16

0 10 -8 2 -58

0 -13 10 -7 59

0 -7 2 -1 13

-2 * row4 + row1;

2 * row4 + row2;

-7 * row4 + row3;

------------------------

1 10 -1 0 -10

0 -4 -4 0 -32

0 36 -4 0 -32

0 -7 2 -1 13

row3 - row2

----------------

1 10 -1 0 -10

0 -4 -4 0 -32

0 40 0 0 0

0 -7 2 -1 13

Per equation #3: y=0

Per equation #2: -4z = -32

z = 8

Per equation #1:

x + -8 = -10

x = -2

Per equation #4:

2(8) - w = 13

16 - w = 13

w = 3

the solution is x=-2, y = 0, z = 8, w=3

(-2,0,8,3)