find the inverse of the coefficient matrix by using row-reduction.

Question

given the following system of equations:
x + y + 5z = 0
2x + y + 9z = 30
x + 2y + 7z = 10

(a) find the inverse of the coefficient matrix by using row-reduction.
(b) check that the matrix which you have just found really is the desired inverse. show the check.
(c) use the inverse matrix which you have found to solve the original system of equations.

Answer 1

Given Equatons are x+y+5z = 0

2x+y+9z = 30

x+2y+7z = 10

Cooefficients of the equations in to matrix form.

 

Comments

The solution is wrong...

See the correct solution below......

Answer 2

a).

Row - reduction method :

The system of equations are

Write the equations in to matrix form.

Ax = B

Start with A next to I.

From the augmented matrix : [ A | I ].

So, the inverse matrix .

Answer 3

Contd......

b).

Note :

The matrix  multiplied by its inverse yields the identity matrix.

.

So, the matrix which we have found  is the desired inverse.

Answer 4

Contd...........

c).

If A is a invertible matrix, the inverse matrix could be used to transform B into X.

.

Where A  is coefficient matrix , X  is variable matrix and B  is constant matrix.

The solution of the system is x = - 130, y = - 70, and z = 40.