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Let L : V → W be a linear transformation between two vector spaces. Show that...

Let L : V → W be a linear transformation between two vector spaces. Show that dim(ker(L)) + dim(Im(L)) = dim(V)

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Answer #1

Any doubt in any step then comment below...i will explain you..

Noteone thing , range (L ) or Im(L) ..both are same .. i use range (L) ..ok.. so dont be confuse.. .

As we know that kernel is subspace of vector V ....

So we start by taking basis of kernel and then extent to form the. basis of V ..

Now we have to show that extra vector which we added to form basis of V , that extra vector form a basis of range (L) ...

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