hw1 - V = { (0 , 1) , (1 , 0) } , W = { (0 , , , 0) } ?...

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Winter 2011 Math 67 Linear Algebra Homework 1 Problem 1. Write down matrix equations of the form Ax = b that come from the integrals Z dx x 2 - 5 x + 6 Z dx x 2 + 9 . The second matrix will have complex (“imaginary”) numbers in it. Both matrices will be 2-by-2. Problem 2. If A = ± a b c d ² and A - 1 = 1 ad - bc ± d - b - c a ² then verify that AA - 1 = A - 1 A = ± 1 0 0 1 ² provided, of course, that ad - bc 6 = 0. Problem 3. Draw the sum of the vectors u = (1 , 0), v = (0 , 2) and w = (1 , - 1) in R 2 . Problem 4. Are the following vector spaces over R , with the usual notion of addition and scalar multiplication:
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Unformatted text preview: V = { (0 , 1) , (1 , 0) } , W = { (0 , , , 0) } ? Problem 1.3. from Axler. Problem 1.4. from Axler. Problem 1.5. from Axler. Problem 1.6. from Axler. (I did this in class, remember?) Problem 1.8. from Axler. (Be as formal as possible. Try to make it seem like your solution is in the textbook. Confused, draw the picture from class of two planes intersecting. The intersection is a subspace, right?) 1...
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