coordinate mapping. Hint: you must first define a basis to start this process! (d) Let H 1 } {[::}{::]} 1 2 1 2 2 1 = span{b,, b.}= span{ Let B = 3 3 Draw a cat if you agree that H is a subspace of M...

Extracted text: coordinate mapping. Hint: you must first define a basis to start this process! (d) Let H 1 } {[::}{::]} 1 2 1 2 2 1 = span{b,, b.}= span{ Let B = 3 3 Draw a cat if you agree that H is a subspace of M and you could say or show why. If not, read Theorem 1 (section 4.1), and see if you see how it applies. 2x2 Draw a dog if you agree that ß is a basis for H you could explain or show why. I 1. -11 35 Find [w]a. That is, find Hint: you don't need to do any more work! 0 78 IB


Extracted text: :} -2 1 2 2 1 (a) Write as a linear combination of the set of matrices -1 3 Do this "directly" without using a coordinate mapping. That is, solve 1 1 11 -2 +b which will lead to a system of equations. %3D -1 1 2 1 y (b) Show that the set does not span V = :x, y, z eR} by 5 3 finding a vector (a matrix in this case) that is in V but is not in 1 span 1 Please make it clear that (or show why) your vector satisfies 0 5 3. the given conditions. Hint: You may use a coordinate mapping, but you need to define your basis and write clear explanations of your findings. 35 -11 35 1 (c) Let b, 1 -11 b, and w= Write %3D as a 5 3 78 78 1 linear combination of 2 and 5 2 1 Solve this by using a 3