Question: Prove each statement Let T : R n R m be a linear transformation. Show that T is injective if and only if T(~x) =

Prove each statement

Let T : R n R m be a linear transformation. Show that T is injective if and only if T(~x) = ~0 has only the trivial solution.

Let T : R n R m be a linear transformation with standard matrix A. Show that T is surjective if and only if the columns of A span R m.

The inverse of a matrix is unique

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