- #1

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Dim(M

_{2x2})= 4, so a basis would have 4 components?

I got this far and am stuck.

[a, b ; c , -a] = a[1,0; 0,-1] + b[0, 1;0,0] +c[0,0; 1,0]

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- Thread starter judahs_lion
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- #1

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Dim(M

I got this far and am stuck.

[a, b ; c , -a] = a[1,0; 0,-1] + b[0, 1;0,0] +c[0,0; 1,0]

- #2

Mark44

Mentor

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A basis for MH = ([a,b;c,d] : a+d =0}

Dim(M_{2x2})= 4, so a basis would have 4 components?

I got this far and am stuck.

[a, b ; c , -a] = a[1,0; 0,-1] + b[0, 1;0,0] +c[0,0; 1,0]

Now, do these matrices span H? I.e., can every matrix in H be written as a linear combination of the three matrices above?

What's left to do is to show that H is a subspace of M

That the zero matrix is in H.

That if A and B are in H, then A + B is in H.

That if A is in H and c is a scalar, then cA is in H.

- #3

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Thank you

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