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My homework involves of identifying all failing Vector Space Axioms for various sets of vector spaces. I did fine with a "regular" set like (x,y,z) which has an operation like k(x,y,z)=(kx,y,z). I have worked through all 10 of the axioms, comparing left sides with right sides to figure out which ones fail.

However, now I have to determine if three matrices fail any Vector Space Axioms. I have no clue on how to do matrices.

Here they are:

[tex]\left(\begin{array}{cc}a&1\\1&b\end{array}\right)[/tex]

[tex]\left(\begin{array}{cc}a&0\\0&b\end{array}\right)[/tex]

[tex]\left(\begin{array}{cc}a&a+b\\a+b&b\end{array}\right)[/tex]

I would appreciate any step by step example of another matrix for like axiom 5 which has to do with finding the zero vector, 0+u=u+0=u where 0 is not zero, but a zero vector or for this instance, a zero matrix. I am not looking for a solution, but a method of solving these vector spaces.

Thank you very much

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# Homework Help: Vector Space Axioms which fail certain matrices

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