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# hw2 - Linear Algebra Homework 2 Selected Solutions Any...

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Unformatted text preview: Linear Algebra Homework 2 Selected Solutions Any mistakes are the sole resposibility of the author–T.Peters 2.3.1c A = 1 3 1 2 1 1- 2 2- 1 . (i) det A = 1 · 1 1 2- 1- 3 · 2 1- 2- 1 + 1 · 2 1- 2 2 = (- 1- 2)- 3(- 2 + 2) + (4 + 2) = 3 (ii) adj A = 1 1 2- 1- 2 1- 2- 1 2 1- 2 2- 3 1 2- 1 1 1- 2- 1- 1 3- 2 2 3 1 1 1- 1 1 2 1 1 3 2 1 T = - 3 0 6 5 1- 8 2 1- 5 T = - 3 5 2 1 1 6- 8- 5 (iii) A- 1 = 1 det A adj A = 1 3 - 3 5 2 1 1 6- 8- 5 = - 1 5 3 2 3 1 3 1 3 2- 8 3- 5 3 2.3.2e x 1 = ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ 0 1 0 1 1 1- 2 0 0 2 1 0 1 0 1 ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ 1 1 0 0 1 1- 2 1 0 2 1 1 1 0 1 ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ =- 2 3 , x 2 = ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ 1 0 0 0 1 1- 2 1 0 2 1 1 0 0 1 ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ 1 1 0 0 1 1- 2 1 0 2 1 1 1 0 1 ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ = 2 3 , x 3 = ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ 1 1 0 0 1 1- 2 1 0 0 1 1 1 0 1 ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ 1 1 0 0 1 1- 2 1 0 2 1 1 1 0 1 ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ = 1 3 , x 4 = ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ 1 1 0 0 0 1 1 1 1 0 2 0 1 1 0 0 ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛ ˛...
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hw2 - Linear Algebra Homework 2 Selected Solutions Any...

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