Question: An m x n matrix A has Null(A) = R if and only if it defines an injective linear transformation TA: Rx - Rm. Suppose

An m x n matrix A has Null(A) = R" if and only if it defines an injective linear transformation TA: Rx - Rm. Suppose T: V - W is a linear transformation, v1, . . . , Un E V, such that Tu], . . . , Tun E W are linearly independent, then v1, . .. , Un are linearly independent. Suppose A is an n x n matrix and b E R". If a system Ax = b has a unique solution, then Arx = b also has a unique solution. An n x n matrix is diagonalizable if and only if it has n distinct eigenvalues

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