Question

What is the solution to the matrix equation [2 1 1 0]x=5/10

Answer 1

[2 1 | 1 0 ] • x = [5 | 10]

We multiply by the inverse of

[2 1 | 1 0 ]

det( [2 1 | 1 0] ) = -1

=> [2 1 | 1 0 ]^(-1) = (-1)•[0 -1 | -1 2 ] =

= [0 1 | 1 -2]

=> [2 1 | 1 0 ] • x = [5 | 10]

=> x = [2 1 | 1 0 ]^(-1) • [5 | 10]

=> x = [0 1 | 1 -2] • [5 | 10]

=> x = [0+10 | 5-20]

=> x = [10 | -15]