I am doing linear algebra and want to fully understand it, not just pass the class. I was recently taught matrix multiplication and decided to look up how it works. The good part is that I understand the concept. Matrices are a way of representing linear transformations. So matrix multiplication is actually a composition of functions. That is why it is not communicative and it is associative.(adsbygoogle = window.adsbygoogle || []).push({});

But i recently came across this article and I could not follow the math near the middle of the page.

http://nolaymanleftbehind.wordpress.com/2011/07/10/linear-algebra-what-matrices-actually-are/

the matrices that are being multiplied are

[ 2 1 ] [ 1 2 ]

[ 4 3 ] [ 1 0 ]

the basis are w1 and w 2

and w1 = [ 1 0 ]

and w2 = [ 0 1 ]

The author states that all that is needed it to see how the linear transformation affects the basis vectors.

Then it states that f(g(w1)) = f(w1+w2)

How does that work? Where on earth do you plug in the w1?

Please help

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# Matrix Multiplication and Function Composition

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