Matrix method

Question

Use a matrix method to solve the set of equations x+2y+3=0 and 3x-y-5=0

Answer 1

First get the equations into another form by just doing a little algebra here

 

x+2y=-3

3x-y=5 Then set up the matrix of coefficients

[1 2 -3]

[3 -1 5]

 

Now you want to get the matrix into reduced row echelon form. Which means on one side you get the identity matrix(the matrix with just 1's on the main diagonal. First operation is -3R₁+R₂. This gives us

 

[1 2 -3]                                                                                                                        [1 2 -3]

[0 -7 14] Now the next pivot is the -7, but we must make that 1 so, divide by -7. -(1/7)R₂ [0 1 -2] 

                           [1 0 1]

-2R₂+R₁ gives us [0 1 -2]

 

The matrix is now in reduced row echelon form. If you read it off we get in row 1; 1x+0y=1, x=1

0x+1y=-2, y=-2