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I am self-learning linear algebra and my textbook asks to simplify the following matrix product with no explanation.

$\begin{pmatrix} \cos\theta & \sin\theta \\ \sin\theta & -\cos\theta \\ \end{pmatrix} \begin{pmatrix} \cos\theta\\ \sin\theta\\ \end{pmatrix}$

Basically I know how to calculate the product of the matrix, etc but what I don't get is how to achieve the answer they have given which is as follows.

$\begin{pmatrix} 1\\ 0\\ \end{pmatrix}$

What is it that I am missing, or is the answer in the book wrong?

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up vote 4 down vote accepted

It's correct. You just need to multiply it out. You will need to apply the trigonometric formula $\cos^2\theta + \sin^2\theta =1.$

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I see what I was doing wrong. I was squaring theta instead of the result. Thanks. Will accept your answer once the time has passed :) – ctor Oct 5 '12 at 21:58
Yeah, I checked it on my graphing calculator just after I posted. Thanks! :D – ctor Oct 5 '12 at 22:02

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