M115A-Review

M115A-Review - MATH 115A - MATH 33A Review Questions Paul...

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Unformatted text preview: MATH 115A - MATH 33A Review Questions Paul Skoufranis September 13, 2011 Instructions: This documents contains a series of questions designed to remind students of the material discussed in MATH 33A. It is recommended that students work through these questions at the beginning of MATH 115A or as material is discussed in MATH 115A. The questions are ordered from easiest to most difficult and are not ordered as material will be covered in MATH 115A. Students who struggle with these questions should review the material or seek help. Question 1) Solve the following system of linear equations (that is, find all solutions to the following system of equations (if any exist)): 3 x 1 + 0 x 2 + x 3 + 91 x 4 =- 121 4 x 1- 9 x 2 + 14 x 3 + x 4 = 0 x 1- 3 x 2 + x 3 + x 4 =- 1 2 x 1- 7 x 2- x 3 + 2 x 4 =- 2 (Hint: Fractions are not your friend.) Question 2) Compute the inverse of the following matrix: A = 1 2 3 2 5 8 0 1 0 Question 3) Let A = 4 10 17 33 1 2 4 8 2 5 10 20 8 20 33 65 B = 7 5 0 3 3 0 2 1 5 7 9- 1 11 0 2 2 (a) Compute det ( A ) using Gauss-Jordan elimination. (b) Compute det ( B ) using the Laplace (cofactor) expansion or using the permutation expansion. (c) Compute det ( BA ). Question 4) Let ~v 1 = 1 1 1 ~v 2 = 1 1 1 ~v 3 = 3 5 and let W = span { ~v 1 ,~v 2 ,~v 3 } . (a) Compute an orthonormal basis for W . (b) Compute the QR-factorization of the matrix M = 1 0 3 1 1 0 1 1 0 0 1 5 ....
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M115A-Review - MATH 115A - MATH 33A Review Questions Paul...

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