For example, if I am given three linearly independent $3 \times 3$ matrices. How would I go about proving that they span, say the set containing all skew symmetric $3 \times 3$ matrices?
Thanks for any help. Linear algebra does my head in.
2026-04-07 09:51:57.1775555517
How to prove that a given basis spans a certain subspace?
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In general we can consider the four matrices as 9-by-1 vectors and perform a RREF or solve the system $av_1+bv_2+cv_3=w$.
In this case note that the subspace of skew symmetric matrices has dimension 6.