00:01
In this example, we're dealing with the m by n matrix that satisfies the homogeneous equation ax equals 0.
00:07
Let's for the sake of an interesting problem, suppose that the vector u in rn has to always match this size here is a solution.
00:27
Let's say what that means for the moment.
00:29
If u in rn is a solution that would mean that a times u where u is in place of x is the zero vector next let's further do the following let c be any scalar and we want to know then is c times u a solution to this same matrix equation a times x equals zero so given that u is a solution we take a scalar c and we're wondering is c times u also a solution? the only way to check and know for sure is to place our c times you here in place of x.
01:15
So here's our check.
01:17
Take the matrix a, multiply it by the vector c times you.
01:22
Now our goal is to make it to the zero vector here.
01:25
If we can't get there, we'll say no, c times you is not a solution.
01:30
If we make it to the zero vector, then we'll say yes, c times u is a solution...