Math121sol7 - Math 121 Linear Algebra and Applications...

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Math 121: Linear Algebra and Applications Prof. Lydia Bieri Solution Set 7 Posted: December 3rd Written by: Luca Candelori Exercise 1 (3.3/4b , 3.3/5) . (a) We can rewrite the system as 1 2 - 1 1 1 1 2 - 2 1 · x 1 x 2 x 3 = 5 1 4 The inverse of the coefficient matrix is given by A - 1 = 1 9 3 0 3 1 3 - 2 - 4 6 1 Applying A - 1 to both sides of the equation above we get x 1 x 2 x 3 = 1 9 3 0 3 1 3 - 2 - 4 6 1 · 5 1 4 = 3 0 - 2 (b) Let n = 2. Then x + y = 1 and 2 x + 2 y = 2 has infinitely many real solutions. Exercise 2 (3.4/2f, 4.2/18,20) . (a) The solutions to the system are all of the form 0 - 3 1 3 + λ 1 - 2 0 1 (b) The first matrix has determinant 10, the second has determinant 17-3i Exercise 3 (3.4/14) . Noone had problems with this exercise, so I will leave the tedious proof to the reader. Exercise 4 (4.4/1a-g) .
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