Linear algebra Matrices

**Linnus** · September 13th 2008, 06:39 PM

Let $T: \Re^2 \rightarrow \Re^2$ be the map that first projects points on to the line $x_2=\sqrt {3}x_1$ than rotates 30 degrees clockwise.

a) Find the matrix representation of T.
b) Find the range of T (describe it).
c) Find the nullset of T (describe it).

Sorry for posting so many problems. I'm new to this subject and I'm confused.
Thank you!

**ThePerfectHacker** · September 13th 2008, 07:08 PM

Originally Posted by Linnus

Let $T: \Re^2 \rightarrow \Re^2$ be the map that first projects points on to the line $x_2=\sqrt {3}x_1$ than rotates 30 degrees clockwise.

a) Find the matrix representation of T.
b) Find the range of T (describe it).
c) Find the nullset of T (describe it).

Sorry for posting so many problems. I'm new to this subject and I'm confused.
Thank you!

The matrix for rotation is $A=\left[ \begin{array}{cc}\cos \theta & \sin \theta \\ - \sin \theta & \cos \theta \end{array} \right]$ .

The matrix for dilations is $B = \left[\begin{array}{cc} \sqrt{3} & 0 \\ 0 & \sqrt{3} \end{array} \right]$ .

Thus, what you are looking for is the matrix product $AB$ .

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