This stuff is confusing. I don't know if it's hard or not, I just have a feeling I don't really know what I'm doing.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

1. Show that the equation Ax=b has a unique solution if and only if the solution to Ax=0 is x=0.

2. Let A be an m x p matrix, and let B be a p x n matrix. Show that the range of A is contained in the range of AB. Show that the kernel of B is contained in the kernel of AB. Is the reverse inclusion true in either case?

2. Relevant equations

1. Ax=b; Ax=0; x=0

2. See below.

3. The attempt at a solution

1. I really have no idea what to do.

2. A=[v1 ... vp]; B=[w1 ... wn]

AB=[Aw1 ... Awn]

im(A)=c1v1 + ... + cpvp

im(AB)=c1Aw1 + ... + cnAwn=A(c1w1 + ... + cnwn)

That's all I have. This is probably not even close to what I'm supposed to be doing. Please help!

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# Linear Algebra Problems (Easy?)

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