Question

Solve the following system of linear equations (using [x]=[A] "[b]): -0.8147x1 + 0.0975x2 + 0.1576x3 + 0.1419x4 + 0.6557x5 = 0.7577 0.9058X1 + 0.2785x2 +0.9706x3 + 0.4218X4 - 0.0357x5 = 0.7431 0.1270x1 + 0.5469x2 + 0.9572x3 + 0.9157x4 - 0.8491x5 = 0.3922 -0.9134x1 + 0.9575x2 + 0.4854x3 - 0.7922x4 + 0.9340x5 = 0.6555 -0.6324x1 + 0.9649x2 + 0.8003x3 + 0.9595x4 - 0.6787X5 = 0.1712 As a check, substitute your answers for X1, X2 ... Xs into the left side of each of the equations above to make sure that the left side is equal to the right side.

In MATLAB please.

Answer 1

%Enter matrix A in the system of linear equations >> A=(-0.8147 0.0975 0.1576 0.1419 0.6557 ; 0.9058 0.2785 0.9706 0.4218 -0.0357 ; 0.1270 0.5469 0.9572 0.9157 -0.8491 ; -0.9134 0.9575 0.4854 -0.7922 0.9340 ; -0.6324 0.9649 0.8003 0.9595 -0.6787] A= Columns 1 through 4 -0.8147 0.9058 0.1270 -0.9134 -0.6324 0.0975 0.2785 0.5469 0.9575 0.9649 0.1576 0.9706 0.9572 0.4854 0.8003 0.1419 0.4218 0.9157 -0.7922 0.9595 Column 5 0.6557 -0.0357 -0.8491 0.9340 -0.6787 Enter matrix B in the given system of linear equations >> B=[0.7577 ; 0.7431 ; 0.3922 ; 0.6555 ; 0.1712] B 0.7577 0.7431 0.3922 0.6555 0.1712 >> |

%Now we have to find the inverse of matrix A and multiply it with matrix B >> X=inv (A) *B Х -0.3925 -0.8950 1.4212 -0.0352 0.4670 >> %The solution to the given system of equations is matrix X >> %To check the solution we have to multiply matrix A and matrix X and we have to obtain matrix B >> Y=A*X Y = 0.7577 0.7431 0.3922 0.6555 0.1712 >> %By multiplying the matrices A and X we got matrix Y which is same as matrix B therefore the obtained solution matrix X is correct