Question: Let A be a 4 4 matrix and let U be its row echelon form. (a) Suppose columns 1, 2. 4 of U form

Let A be a 4 × 4 matrix and let U be its row echelon form.
(a) Suppose columns 1, 2. 4 of U form a basis for its range. Do columns 1, 2,4 of A form a basis for its range? If so. explain why; if not, construct a counterexample.
(b) Suppose rows 1, 2, 3 of U form a basis for its corange. Do rows 1, 2, 3 of A form a basis for its corange? If so, explain why; if not, construct a counterexample.
(c) Suppose you find a basis for kertU. Is it also a basis for ker A?
(d) Suppose you find a basis for coker U. Is it also a basis for coker A?

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a Yes This is our method of constructing the basis for the range and the proof is out lined ... View full answer

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