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Well I hope it's not a thread that already is in the storage here. I want to understand the image of a matrix. not only calculating it but also why I'm doing that. Here are my questions:

1) They say d = Lx has a solution if d ∈ ImL. I know that the image of a matrix is calculated by Lx = x. but here we have d = Lx.

2) Can anybody show me what image of a matrix and what solution the question above has geometrically? I mean by firgures?

3) If A is a nxn matrix and B is a nx1 matrix and you only have the image of A , what does it say above the image of Γ = [B, AB]?

4) If We know the image of A and B where both A and B are nxn. what do you know about the image of C=AB , C = A+B?

and last question which doesnt have so much to do with image:

5) When is the product of two matrices symmetric? by only looking at them?

I appritiate all kind of help. thanks in advance

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# Image of a Matrix and symmetric matrix

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