Problem to solve
Solve \[-x+3y+2z=5\], \[-3x-2y+z=-4\], \[x-y+z=3\]
Solution
STEP 1
Solve the following system:
{-x + 3 y + 2 z = 5
-3 x - 2 y + z = -4
x - y + z = 3
STEP 2
Express the system in matrix form:
(-1 | 3 | 2
-3 | -2 | 1
1 | -1 | 1)(x
y
z) = (5
-4
3)
STEP 3
Solve the system with Cramer's rule:
x = 5 | 3 | 2
-4 | -2 | 1
3 | -1 | 1/-1 | 3 | 2
-3 | -2 | 1
1 | -1 | 1 and y = -1 | 5 | 2
-3 | -4 | 1
1 | 3 | 1/-1 | 3 | 2
-3 | -2 | 1
1 | -1 | 1 and z = -1 | 3 | 5
-3 | -2 | -4
1 | -1 | 3/-1 | 3 | 2
-3 | -2 | 1
1 | -1 | 1
STEP 4
Evaluate the determinant -1 | 3 | 2
-3 | -2 | 1
1 | -1 | 1 = 23:
x = 5 | 3 | 2
-4 | -2 | 1
3 | -1 | 1/23 and y = -1 | 5 | 2
-3 | -4 | 1
1 | 3 | 1/23 and z = -1 | 3 | 5
-3 | -2 | -4
1 | -1 | 3/23
STEP 5
Evaluate the determinant 5 | 3 | 2
-4 | -2 | 1
3 | -1 | 1 = 36:
x = 36/23 and y = -1 | 5 | 2
-3 | -4 | 1
1 | 3 | 1/23 and z = -1 | 3 | 5
-3 | -2 | -4
1 | -1 | 3/23
STEP 6
Evaluate the determinant -1 | 5 | 2
-3 | -4 | 1
1 | 3 | 1 = 17:
x = 36/23 and y = 17/23 and z = -1 | 3 | 5
-3 | -2 | -4
1 | -1 | 3/23
STEP 7
Evaluate the determinant -1 | 3 | 5
-3 | -2 | -4
1 | -1 | 3 = 50:
Answer: | 
 | x = 36/23 and y = 17/23 and z = 50/23