Mathematics, 10.07.2019 02:20, vane8229

(1) (20 points) let a be an n x n matrix. determine which (if any) of the statements are equivalent to the statement the matriz a is invertible. (a) the columns of a are linearly independent. (b) the columns of a span r". (c) the null space ofa is trivial, ie. nul(). (d) there is only one solution to the equation ax = 0 and it is the x = 0. (e) the unique linear map ta : rn ? rn, defined by a, is one-to-one. ) the unique linear map ta : rn ? rn, defined by a, is onto. (g) the rank of a is n. j (h) det a0.

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(1) (20 points) let a be an n x n matrix. determine which (if any) of the statements are equivalent...