Fm241sol1 - M241 Matrix Algebra Homework Assignment 1 Answers Graded Problems Section 1.2 Problem 4 Section 1.3 Problems 10 and 12 Section 1.4

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Unformatted text preview: M241: Matrix Algebra Homework Assignment 1 Answers Graded Problems: Section 1.2 Problem 4; Section 1.3 Problems 10 and 12; Section 1.4 Problems 2 and 38; Section 1.5 Problem 4. Section 1.2. Problem 4. No solution; zero right sides produce 3 lines through origin; right sides 1, 1, 0 give x = 1 and y = 0; right sides 2, -1, 1 give x = 0 and y = 1; any combination is solvable. Problem 8. eq(1)-eq(2)+eq(3) gives 0=1; change 0 to -1; (3 ,- 1 , 0) is a solution. Problem 22. An example is ( a,b ) = (3 , 6) and ( c,d ) = (1 , 2). If ( a,b ) = k ( c,d ) and abcd 6 = 0, then k = a/c = b/d . Now a/c = b/d implies that ad = bc and thus a/b = c/d . Thus ( a,c ) = l ( b,d ), where l = a/b = c/d . Q.e.d. Section 1.3. Problem 1. Multiply by l = 10 / 2 = 5 and subtract to find 2 x + 3 y = 1 and- 6 y = 6. The pivots are 2 and- 6. Problem 4. Subtract l = c/a times equation 1. The new second pivot multiplying y is d- cb a = ad- bc a ....
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This note was uploaded on 09/30/2010 for the course MATH 21-241 taught by Professor Irina during the Fall '08 term at Carnegie Mellon.

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Fm241sol1 - M241 Matrix Algebra Homework Assignment 1 Answers Graded Problems Section 1.2 Problem 4 Section 1.3 Problems 10 and 12 Section 1.4

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