Blog: `5x - 5y = -5, -2x - 3y = 7` Use matricies to solve the system of equations (if possible). Use Gauss-Jordan elimination.

Sunday, March 17, 2013

Given system of equations are

5x - 5y = -5, -2x - 3y = 7

so ,we get the matrices as

A = $\displaystyle{\left[\matrix{{5}&-{5}\\-{2}&-{3}}\right]}$

and

B = $\displaystyle{\left[\matrix{-{5}\\{7}}\right]}$

the augmented matrix [AB] = $\displaystyle{\left[\matrix{{5}&-{5}&-{5}\\-{2}&-{3}&{7}}\right]}$

on solving the [AB] we get the values of x,y

Step 1. Make the pivot in the 1st column by dividing the 1st row by 5

$\displaystyle{\left[\matrix{{1}&-{1}&-{1}\\-{2}&-{3}&{7}}\right]}$

step 2. Multiply the 1st row by -2

$\displaystyle{\left[\matrix{-{2}&{2}&{2}\\-{2}&-{3}&{7}}\right]}$

step 3. Subtract the 1st row from the 2nd row

$\displaystyle{\left[\matrix{{1}&-{1}&-{1}\\{0}&-{5}&{5}}\right]}$

step 4. divide the second row with -5 we get

$\displaystyle{\left[\matrix{{1}&-{1}&-{1}\\{0}&-{1}&{1}}\right]}$

Step 5. subtract the 2 nd row from 1st row we get

$\displaystyle{\left[\matrix{{1}&{0}&-{2}\\{0}&-{1}&{1}}\right]}$

step 6. multiply the 2 nd row with -1

$\displaystyle{\left[\matrix{{1}&{0}&-{2}\\{0}&{1}&-{1}}\right]}$

so the vlaues of x,y are x= -2 , y =-1

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