- #1

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are vectors in R^n. Show that if Au = Av and

u ≠ v, then A is not invertible.

This is the book's proof:

From the fact that Au = Av, we have A(u − v) = 0. If

A is invertible, then u − v = 0, that is, u = v, which

contradicts the statement that u = v.

Mine proof is, if A is invertible thus A^-1 exists

(A^-1)(Au)=(A^-1)(Av)

A^-1*A=I

→u=v

if u≠v then then the above does not hold, implying that A^-1 does not exist.