In this case the column space of A is a line with parametric vector form x = λb where b = (2, 1, 2).
For the matrix A =
4 2 4
12 6 12
16 8 16
the set beR3: b = Ax for some x eR3 is the column space of A. The vector v = y belongs to this set whenever the augmented matrix
2 4 2 4 x
12 6 12 y
16 8 16
has:
- a unique solution
There are two linear conditions that must be satisfied, namely:
{0 = 2b + 6, 0 = 8 - 2}
Note: enter the conditions above in the form of a set
e.g. {x + 2y + 3z = 0, x - 2y = 0}
