How do I find the matrix A to the linear transformation T: R^3 --> R^3

it's defined by;

1. reflection against 3x - 6y + 5z = 0

then

2. projection onto 2x + 6y + 4z = 0

Printable View

- Apr 28th 2008, 09:37 AMweasley74linear transformation
How do I find the matrix A to the linear transformation T: R^3 --> R^3

it's defined by;

1. reflection against 3x - 6y + 5z = 0

then

2. projection onto 2x + 6y + 4z = 0 - Apr 28th 2008, 11:00 AMOpalg
Here are the formulas that you need (I won't do the actual question for you).

Suppose that is a unit vector (so that ). Then the projection onto the one-dimensional subspace spanned by**n**is .

If px + qy + rz = 0 is the equation of a plane, let**n**be a unit vector orthogonal to the plane. So . Then the matrix of the projection onto the plane is , and the matrix of the reflection in the plane is .

To find the matrix for the composition of two such operations, form the matrices for each operation, then multiply them. So the matrix for reflection in 3x - 6y + 5z = 0 followed by projection onto 2x + 6y + 4z = 0 is , where**m**and**n**are the normalised versions of (3,-6,5) and (2,6,4) respectively. - Apr 29th 2008, 10:38 AMweasley74
I keep messing this one up, I've done it ten times and I still get the wrong answer.. Help?

- Apr 29th 2008, 11:42 AMOpalg
Unless I've also messed it up, you should get

,

,

.

So the answer should be (I'm not prepared to do the arithmetic to evaluate that). - Apr 29th 2008, 12:39 PMweasley74