Matrix

Question

-4y+3x=-1                       -4x+3y= -2

2x-3y=-3                          -2x-3y=4

the two system of equations above share the same common coefficient matrix a. Because of this, we can use the same inverse to solve both systems of equations as outlined below.

a) find the inverse of the common coefficient matrix A.    

 A^-1

b) find the solutions to th 2 systems by evaluating A^-1B where B represents the right hand side(ie:B=[-1,-3] for the first and B=[-2,4] for the second system.

first system: x= ____________,y=______________

second system x=__________,y=__________

Answer 1

(1)

Step 1:

The first system equations are

Write the equations into matrix form , where is coefficient matrix,

is variable matrix and is constant matrix.

Definition of inverse matrix :

If is an then , where .

Let , then .

, then has an inverse.

(a)

Find the inverse matrix .

(b)

Find values of first system.

Substitute .

Solution:

(a) The inverse matrix is

(b) The value of first system is .

Answer 2

(2)

Step 1:

The second system equations are

Write the equations into matrix form , where is coefficient matrix,

is variable matrix and is constant matrix.

Definition of inverse matrix :

If is an then , where .

Let , then .

, then has an inverse.

(a)

Find the inverse matrix .

(b)

Find values of second system.
 

Substitute .

Solution:

(a) The inverse matrix is

(b) The value of second system is .