Sunday, March 17, 2013

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

Given system of equations are


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


so ,we get the matrices as


A = `[[5, -5], [-2, -3]]`


and


B = `[[-5], [7]]`


the augmented matrix [AB] = `[[5, -5, -5], [-2, -3, 7]]`




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


`[[1, -1, -1], [-2, -3, 7]]`



step 2. Multiply the 1st row by -2


`[[-2, 2, 2], [-2, -3, 7]]`



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


`[[1, -1, -1], [0, -5, 5]]`



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


`[[1, -1, -1], [0, -1, 1]]`



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


`[[1, 0, -2], [0, -1, 1]]`



step 6. multiply the 2 nd row with -1


`[[1, 0, -2], [0, 1, -1]]`




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

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