Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The matrix is:

cos(pi/3) 0

sin(pi/3) 0

I have no clue what to put. No solution?

share|improve this question
1  
The preimage is a set, not necessarily just a single vector. –  Jonathan Oct 3 '12 at 3:30

1 Answer 1

up vote 1 down vote accepted

Assuming the vector you're given is $(y_1,y_2)^\intercal$, try writing out the multiplication $$\left( \begin{array}{cc} \cos{\pi/3} & 0 \\ \sin{\pi/3} & 0 \end{array} \right)\left( \begin{array}{c} x_1 \\ x_2 \end{array} \right)=\left( \begin{array}{c} y_1 \\ y_2 \end{array} \right)$$ and describe the set of vectors $(x_1,x_2)^\intercal$ which satisfy that criteria.

share|improve this answer
    
I found x1 and x2. Are you saying I now need to find them under T? –  Grace C Oct 3 '12 at 4:45
    
Or would x1 and x2 alone be a preimage? –  Grace C Oct 3 '12 at 4:47
    
When you multiply out the LHS you get two equations, $\cos{\pi/3}x_1=y_1$ and $\sin{\pi/3}x_1=y_2$. These two equations only depend on $x_1$, so assuming a solution exists, the preimage will be the set of matrices with first entry as the value of $x_1$ given by those equations and any second entry you want (because it doesn't matter what $x_2$ you pick, it just gets multiplied by 0 anyway). –  Alexander Gruber Oct 3 '12 at 21:06

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.