SOLUTION: Please help me with this problem. Use inverse Matrix to Solve Linear System. 3x - 7y = -16 -2x+ 4y = 8 Thanks a lot for your time.

Algebra ->  Matrices-and-determiminant -> SOLUTION: Please help me with this problem. Use inverse Matrix to Solve Linear System. 3x - 7y = -16 -2x+ 4y = 8 Thanks a lot for your time.       Log On


   

Question 18317: Please help me with this problem.
Use inverse Matrix to Solve Linear System.
3x - 7y = -16
-2x+ 4y = 8
Thanks a lot for your time.
KAt
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
3x - 7y = -16
-2x+ 4y = 8
we write this eqn.as A*X=B,then find A^-1 and use it to premultiply B to get X.
we have A = matrix%282%2C2%2C3%2C-7%2C-2%2C4%29
X=matrix%282%2C1%2Cx%2Cy%29 and
B=matrix%282%2C1%2C-16%2C8%29
we get inverse matrix of A =A^-1..by the following steps..
1..take minors of each element..that is the determinant obtained by deleting the row and column containing the element under consideration..
we have minor of 3 designated as m(3)
m(3)=4
m(-7)=-2
m(-2)=-7
m(4)=3
2.now find cofactors of each element .they are minors multiplied by (-1)^(sum of row and column numbers of the element under consideration.let us designate them as c(3)etc..
c(3)=[(-1)^(1+1)]*4=4
c(-7)=[(-1)^(1+2)]*(-2)=2
c(-2)=[(-1)^(2+1)]*(-7)=7
c(4)=[(-1)^(2+2)]*(3)=3
3.make a matrix replacing each element in the original matrix by its cofactor.
we get matrix%282%2C2%2C4%2C2%2C7%2C3%29
4.now make a transpose of the above matrix..that is interchange rows and columns.
we get matrix%282%2C2%2C4%2C7%2C2%2C3%29
5.now devide the above matrix with determinant of original matrix to get the inverse
determinant of A =3*4-(-7)(-2)=12-14=-2
so inverse of A = (-1/2)*matrix%282%2C2%2C4%2C7%2C2%2C3%29
...lastly we use this to multiply B to get X.so
X=matrix%282%2C1%2Cx%2Cy%29 =(-1/2)*matrix%282%2C2%2C4%2C7%2C2%2C3%29*
*matrix%282%2C1%2C-16%2C8%29
=(-1/2)*matrix%282%2C1%2C%28-64%2B56%29%2C%28-32%2B24%29%29
=matrix%282%2C1%2C4%2C4%29
hence x=4 and y=4