Answer:
x = -2
, y = 3
, z = -5 thus the answer is C.)
Step-by-step explanation:
Solve the following system:
{3 x + 2 y - 3 z = 15
-2 x + 4 y + 2 z = 6
4 z + 12 = -8
Express the system in standard form:
{3 x + 2 y - 3 z = 15
-2 x + 4 y + 2 z = 6
0 + 0 + 4 z = -20
Express the system in matrix form:
(3 | 2 | -3
-2 | 4 | 2
0 | 0 | 4)(x
y
z) = (15
6
-20)
Write the system in augmented matrix form and use Gaussian elimination:
(3 | 2 | -3 | 15
-2 | 4 | 2 | 6
0 | 0 | 4 | -20)
Add 2/3 × (row 1) to row 2:
(3 | 2 | -3 | 15
0 | 16/3 | 0 | 16
0 | 0 | 4 | -20)
Multiply row 2 by 3/16:
(3 | 2 | -3 | 15
0 | 1 | 0 | 3
0 | 0 | 4 | -20)
Divide row 3 by 4:
(3 | 2 | -3 | 15
0 | 1 | 0 | 3
0 | 0 | 1 | -5)
Subtract 2 × (row 2) from row 1:
(3 | 0 | -3 | 9
0 | 1 | 0 | 3
0 | 0 | 1 | -5)
Add 3 × (row 3) to row 1:
(3 | 0 | 0 | -6
0 | 1 | 0 | 3
0 | 0 | 1 | -5)
Divide row 1 by 3:
(1 | 0 | 0 | -2
0 | 1 | 0 | 3
0 | 0 | 1 | -5)
Collect results:
Answer: {x = -2
, y = 3
, z = -5
