(a) (13 points) Find a 4 x 4 matrix C such that (i) C is not...

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(a) (13 points) Find a 4 x 4 matrix C such that (i) C is not invertible, and (ii) every entry of C is nonzero. (b) (12 points) Does there exist a 52 matrix A and a 25 matrix B such that AB is invert Either provide a 5x2 matrix A and a 2x5 matrix B such that AB is invertible, or other show that for every 52 matrix A and every 25 matrix B the product AB is not invert (a) (13 points) Find a 4 x 4 matrix C such that (i) C is not invertible, and (ii) every entry of C is nonzero. (b) (12 points) Does there exist a 52 matrix A and a 25 matrix B such that AB is invert Either provide a 5x2 matrix A and a 2x5 matrix B such that AB is invertible, or other show that for every 52 matrix A and every 25 matrix B the product AB is not invert