Sunday, January 22, 2017

`8x - 4y = 7, 5x + 2y = 1` Use matricies to solve the system of equations (if possible). Use Gauss-Jordan elimination.

Given system of equations are


`8x - 4y = 7, 5x + 2y = 1`


so the matrices A and B are given as follows


A = `[[8, -4], [5, 2]]`


B = `[[7], [1]]`


so the augmented matrix is [AB] = `[[8, -4, 7], [5, 2, 1]]`


on solving this we get the values of x,y .


step 1 .  Make the pivot in the 1st column by dividing the 1st row by 8


`[[1, -1/2, 7/8],...

Given system of equations are


`8x - 4y = 7, 5x + 2y = 1`


so the matrices A and B are given as follows


A = `[[8, -4], [5, 2]]`


B = `[[7], [1]]`


so the augmented matrix is [AB] = `[[8, -4, 7], [5, 2, 1]]`


on solving this we get the values of x,y .


step 1 .  Make the pivot in the 1st column by dividing the 1st row by 8


`[[1, -1/2, 7/8], [5, 2, 1]]`



step 2 . muptiply the 1st row by 5


`[[5, -5/2, 35/8], [5, 2, 1]]`



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


`[[1, -1/2, 7/8], [0, 9/2, -27/8]]`



step 4 divide the second row by 9/2


`[[1, -1/2, 7/8], [0, 1, -3/4]]`



step 5 multiply the 2nd row by -1/2  and subtract the 2nd row from the 1st row


 `[[1, 0, 1/2], [0, 1, -3/4]]`



so, the values of x, y are x= 1/2 and y = -3/4


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