Practice Midterm 1 (Vojta) - Math 54 Sample First Midterm 1 1(10 points Find the inverse of the matrix A = 2 1 introduced in Chapter 2 2 2 6 1 3 7 if it

Practice Midterm 1 (Vojta) - Math 54 Sample First Midterm 1...

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Math 54 Sample First Midterm 1. (10 points) Find the inverse of the matrix A = 1 2 3 2 6 7 1 1 2 , if it exists. Use the algorithm introduced in Chapter 2. 2. (10 points) A matrix A and an echelon form of A are given here: A = 1 2 - 1 1 - 1 - 2 - 4 3 - 3 0 1 2 - 3 3 3 1 2 - 2 2 1 1 2 - 1 1 - 1 0 0 1 - 1 - 2 0 0 0 0 0 0 0 0 0 0 . (a). Write the solution set of the homogeneous system A~x = ~ 0 in parametric vector form (i.e., as a linear combination of fixed vectors, in which the weights are allowed to take on arbitrary values). (b). Give a basis of Nul A . (c). Give a basis of Col A . 3. (12 points) Let ~v 1 = 0 1 0 0 , ~v 2 = 2 0 3 - 1 , and ~v 3 = 4 1 6 - 2 . Let H = span { ~v 1 ,~v 2 ,~v 3 } . (a). Find a subset of { ~v 1 ,~v 2
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  • Spring '08
  • Chorin
  • Math, Linear Algebra, −1, parametric vector form

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