Prove that the set $B = \left\{ \begin{bmatrix}a&b\\c&d\end{bmatrix} | a,b,c,d ∈ \mathbb{Z}\right\}$ is not a subspace of $M(2,2)$.
Is M2x2 a subpace of itself?
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$\begingroup$
vector-spaces
invariant-subspace
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0What is the definition of $M(2,2)$? You might also want to think about the definition of a subspace. Make more effort and edit the question to show what you did. That might help it get reopened. – 2017-01-15
1 Answers
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If you take an element of $B$ and multiply it by a scalar, it must yield another element of $B$. What happens if you choose the scalar to be $\sqrt{2}$?