00:01
In this example, we have the transformation where x is mapped to the matrix a times x, where a is defined as follows.
00:09
Here, the goal is to determine which vectors x are mapped to the zero vector, which in this case would be the 3 by 1, zero vector.
00:31
Well, given the transformation, x maps to ax, what we need to do is determine which vectors x, result in the mapping being sent to the zero vector.
00:43
So really we're just considering the matrix equation, 8 times x equals 0.
00:47
This can be solved by forming the augmented matrix, which will have columns 102, negative 4, 1, negative 6, 7, negative 4, negative 5, 3, negative 4, augmented from here with the 0 vector.
01:04
Now for our next steps, in order to solve for x, we're going to row reduced into row reduced echelon form.
01:15
So for our first pivot, located here, we already have a zero below, but we need to eliminate this entry.
01:22
So let's copy row 1, then to eliminate this entry, well maybe first copy row 2 as well, then to eliminate this entry 2 here, we can multiply row 1 by negative 2 and add it to row 3.
01:42
We obtain 0, 2, negative 8, 6, and 0.
01:52
Now we're in good shape.
01:55
At this pivot position, we need to eliminate the entry here and here.
01:59
So let's make that our next set of row operations...