Question

Use an inverse matrix to solve for the system of equations.

4y+7z=14



−6x−2z=10



x+2y+8z=−3



*This question is worth four points. In order to receive full credit, you must show your work or justify your answer.



[0 5 −3]



[−24 −4]



[−17 −2]



[−4 3 1]

Answer 1

(-1, 7, 2)

Explanation:

we suppose that ax + by + cz = d for the matrix

D = det [ 0 4 7] = 100

-6 0 -2

1 2 8

Dx= det [ 14 4 7] = - 100

10 0 -2

-3 2 8

Dy= det [ 0 14 7] = 700

-6 10 -2

1 -3 8

Dz = det [ 0 4 14] = 200

-6 0 10

1 2 -3

So the solution is:

x = Dx/D = -1, y = Dy/D= 7, z =Dz/D = 2

(-1, 7, 2)

have a good day!