Linear algebra projection question

[turbowaffle]

I hope I posted this in the right section, I didn't see anything specific to linear algebra.

The question is pretty straight forward:

Find the project matrix that transforms vector 2,3 into 2,0.

I can do it sort of intuitively by drawing both vectors, but I can't seem to find the answer algebraicly.

I know that the projection of vector X onto L is (x . u)*u
That is, the dot product of x and u (u is a unit vector parallel to L) multiplied by u. This becomes the 2x2 matrix:

u1^2 u1*u2
u1*u2 u2^2

If we call this matrix A, and I multiply vector <2,3> by this matrix, a set of second degree equations, which I can't solve as a linear system of equation (since u1 and u2 both have an exponant of 2).

Any idea how I am supposed to approach this?

 

[daon]

What about:

[1 0]
[0 0]

 

[JakeD]

I hope I posted this in the right section, I didn't see anything specific to linear algebra.

The question is pretty straight forward:

Find the project matrix that transforms vector 2,3 into 2,0.

I can do it sort of intuitively by drawing both vectors, but I can't seem to find the answer algebraicly.

I know that the projection of vector X onto L is (x . u)*u
That is, the dot product of x and u (u is a unit vector parallel to L) multiplied by u. This becomes the 2x2 matrix:

u1^2 u1*u2
u1*u2 u2^2

If we call this matrix A, and I multiply vector <2,3> by this matrix, a set of second degree equations, which I can't solve as a linear system of equation (since u1 and u2 both have an exponant of 2).

Any idea how I am supposed to approach this?

The matrix \(\displaystyle \L P(x) = x(x'x)^{-1}x'\) will project onto \(\displaystyle \L x.\) \(\displaystyle \L x\) denotes a column vector whose transpose \(\displaystyle \L x'\) is a row vector. \(\displaystyle \L x'x\) is just the dot product. \(\displaystyle \L P(x)\) here turns out to be the matrix that Daon gave.