m241rev1 - M241 Matrix Algebra Midterm 1 Practice Problems...

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M241: Matrix Algebra Midterm 1 Practice Problems Textbook. The answers to all these problems are at the end of the book. Section 1.3 Problems 23, 31. Section 1.4 Problems 1, 11, 13, 41. Section 1.5 Problems 15, 27, 29. Section 1.6 Problems 11, 41, 43. Section 2.1 Problem 21. Section 2.2 Problems 35, 53. Section 2.3 Problems 7, 9. Problem 1. Solve the systems below: x 1 +2 x 2 +3 x 3 +5 x 4 = 2 , 2 x 1 +4 x 2 +8 x 3 +12 x 4 = 6 , 3 x 1 +6 x 2 +7 x 3 +13 x 4 = 4 . 3 x 2 - 6 x 3 +6 x 4 +4 x 5 = - 5 , 3 x 1 - 7 x 2 +8 x 3 - 5 x 4 +8 x 5 = 9 , 3 x 1 - 9 x 2 +12 x 3 - 9 x 4 +6 x 5 = 15 . x 1 +2 x 2 +3 x 3 = 1 , 2 x 1 +3 x 2 +5 x 3 = 1 , 4 x 1 +7 x 2 +11 x 3 = 5 . Problem 2. Let A = 1 2 3 0 2 1 - 1 2 5 4 1 4 . Let ¯ b = b 1 b 2 b 3 . Give all the values of b 1 , b 2 , b 3 for which the system A ¯ x = ¯ b has at least one solution.
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Find the nullspace and the column space of A . Write the general solution of
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m241rev1 - M241 Matrix Algebra Midterm 1 Practice Problems...

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