rue or False: A is onto iff the columns of A span R". True or False:...

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rue or False: A is onto iff the columns of A span R. True or False: If m- n, then A, necessarily a square matrix, is inverti

1. An m × n matrix A=[ai a2 an can be viewed as a function from Rn to Rm, sending x = (xi, , an) e Rn to Ax =

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A. TRUE if A is a n x n or, n x m matrix. If the columns of A span Rⁿ , then every b ∈Rⁿ is a linear combination of the columns of A so that the linear transformation represented by A is onto.

B. TRUE. The linear transformation represented by A is onto as the columns of A span Rⁿ. Also, the n columns of A will span Rⁿ if and only if these n columns are linearly independent. Hence the linear transformation represented by A is one-to-one.

1. TRUE. Every linear transformation T : Rⁿ → R^m can be represented by a unique m × n matrix A. The m rows are the coefficients from the linear combinations of the function form coordinates in R^m.

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