Question

How do you solve `Ax=B` given `A=((2, 0, 0), (-1, 2, 0), (-2, 4, 1))` and `B=((4), (10), (11))`?

Answer 1

Column vector `x=[(x),(y),(z)]=[(2),(6),(50)]`

Explanation:

You may regain the original system of linear equations represented in the given matrix form by applying the definition of matrix multiplication using the Euclidean inner product in `RR^3`, together with the definition of matrix equality to obtain :

`2x+0y+0z=4` .......1.
`-x+2y+0z=10` .......2.
`-2x+4y+z=11` ........3.

where `x` is the column vector `x=[(x),(y),(z)]`.

Solving equation 1 we get `x=2`.

Substituting this into equation 2, we get `y=6`.

Substituting this into equation3 we get `z=50`.