Question: please assist with this problem 1. Let A be an mn matrix with entries win the finite field Fq. Fill in the blanks in the

please assist with this problem

1. Let A be an mn matrix with entries win the finite field Fq. Fill in the blanks in the following statements. (a) The columns of A span Fqm1 iff A has a pivot position in every (b) The columns of A are linearly dependent iff at least one of A does not contain a pivot. (c) The equation AX=0 has no nontrivial solutions iff there is a pivot in every of A. (d) The equation AX=0 has infinitely many solutions iff at least one of A does not have a pivot

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