Question

Show that the set GLm,n(R) of all mxn matrices with the usual matrix addition and scalar...

Show that the set GLm,n(R) of all mxn matrices with the usual matrix addition and scalar multiplication is a finite dimensional vector space

with dim GLm,n(R) = mn.

Show that if V and W be finite dimensional vector spaces with dim V = m and dim W = n, B a basis for V and C a basis for W then

hom(V,W)-----MatB--->C(-)--------> GLm,n(R) is a bijective linear transformation. Hence or otherwise, obtain dim hom(V,W).

Thank you!

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