Mathematics, 07.03.2020 03:04 BreBreDoeCCx

Question 1 (5 points): Let A be an 20 × 20 matrix. (a) Suppose that A has 20 pivot positions. Does the matrix A−1 exist? Explain your answer. (b) Suppose that the columns of A are linearly independent. How many pivot positions does A have? Explain your answer. (c) Suppose that the columns of A are linearly independent. For which vectors b is the equation Ax = b consistent? Explain your answer. (d) Suppose that A−1 exists. How many solutions are there of the equation Ax = b? Explain your answer? (e) Suppose that A has a free variable. Does A−1 exist? Explain your answer.

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Question 1 (5 points): Let A be an 20 × 20 matrix. (a) Suppose that A has 20 pivot positions. Does t...