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## Homework Statement

Let V be a finite dimensional vector space, and let T be a linear map defined on V.

ker T [tex]\subseteq[/tex] V and Im T [tex]\cong[/tex] V/kerT

Let (y_1, . . . , y_k) be a basis of ker T. Augment this list by (x_k+1, . . . , x_n) to a basis for V: (y_1, . . . , y_k, x_k+1, . . . , x_n).

Now here's the part that's getting me:

"Obviously, (x_k+1, . . . , x_n) forms a basis of V/kerT"

## Homework Equations

ker T [tex]\subseteq[/tex] V and Im T [tex]\cong[/tex] V/kerT

## The Attempt at a Solution

I believe that span(x_k+1, . . . , x_n) is isomorphic to V/kerT (they have the same dimension), but I don't see how (x_k+1, . . . , x_n) actually forms a basis for V/kerT