00:01
In this question, we will be looking for the standard matrix for the projection of a 2 vector onto the y -axis in 2 -space.
00:14
Recall that the least squares solution to the system ax equals b is given by a transpose a inverse a transpose b, given that a has linearly independent columns.
00:38
And also recall that a times this least squares solution will be the projection of b onto the column space of a.
00:57
Now, how do we find, or sorry, my mistake, i just want to write out this matrix product here.
01:17
And there we go.
01:18
So how do we use this to find the standard matrix for the projection onto the y -axis? well, note that the y -axis can be interpreted as the column space of a matrix a, and then this formula will be the formula that tells us the projection of the matrix, or sorry, the vector b onto the y -axis.
01:47
And then because we have this transformation expressed as a matrix multiplied by the vector we're operating on, the standard matrix for this operator is just this matrix product here.
02:03
So our steps are to express y as the column space, express the y -axis as the column space of a matrix a, and then compute this product for that matrix...