By using a system of equations, we will see that the solution is:
x = 25, y = -50, z = -15
How to solve the matrix equation?
We can write this as a system of equations:
4x + 2y - z = 15
x + y - z = -10
-3x - y + z = 60
Notice that if we add the second and third equations, we get:
(x + y - z) + (-3x - y + z ) = -10 + 60
-2x = 50
x = 50/-2 = -25
So we already got the value of x. Replacing that in the second equation we et:
25 + y - z = -10
Isolating y we get:
y = -10 - 25 + z = z - 35
Now we can replace that in the first equation:
4x + 2y - z = 15
4*25 + 2*(z - 35) - z = 15
100 + z - 70 = 15
z = 15 - 100 + 70 = -15
And using:
y = z - 35 = -15 - 35 = -50
Then the soution to the matrix equation is:
x = 25, y = -50, z = -15
If you want to learn more about matrix equations:
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