Question

How do you solve the system `w+4x+3y-11z=42` , `6w+9x+8y-9z=31` and `-5w+6x+3y+13z=2`, `8w+3x-7y+6z=31`?

Answer 1

`((w),(x),(y),(z)) = ((-12054/4889),(38342/4889),(-31301/4889),(-14357/4889))`

Explanation:

Rewrite the equation in linear vector and matrix form:
`((1,4,3,-11), (6,9,8,-9), (-5,6,3,13 ), (8,3,-7,6 )) ((w ),(x ), (y ), (z ))= ((42 ),(31 ), (2 ), (31 ))`
Now use gauss elimination to solve the matrix equation. THe goal here is the convert the 4x4 matrix in half diagonal matrix and solve back from the half diagonal... Used a calculator on Matrix mode to solve:
`((w),(x),(y),(z)) = ((-12054/4889),(38342/4889),(-31301/4889),(-14357/4889))`