Solve the following equations using matrices.

Question

-x+y+z=-2 -x+5y-19z=-30 7x-5y-17z=0?

Answer 1

The equations are - x  + y  + z  = -2

- x  + 5y - 19z  = - 30

7x - 5y  - 17z  = 0

Convert the equations into matrix form AX  = B.

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

Now solve the equations in Cramer's method.

The augmented matrix is

The last row of the above augmented matrix is all zeros.

Hence there are infinite number of solutions.

Answer 2

Contd...

In this case z  is a free variable.

We solve any other of the set by assigning one variable in the remaining two equations and then solving for the other two.

Using first row, the equation is  x - 6z = - 5 ---> (1)

Using second row, the equation is y - 5z = - 7 ---> (2)

If z  = 2

Substitute z  = 2 in equation (1).

x  - 6(2) = - 5

x  = - 5 + 12

x  = 7

Substitute z  = 2 in equation (2).

y  - 5(2) = - 7

y  - 10 = - 7

y  = - 7 + 10

y  = 3.