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Course: PHZ 3113, Fall 2010
School: FAU
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(PHZ) Physics 3113 Mathematical Physics Florida Atlantic University Fall, 2009 Review Problems II Recommended Reading: Chow, Appendix 2; Boas, Sections 3.13.3. 1. (Chow A2.1, p. 540) Solve the system 2x y + 2z = 2 x + 10y 3z = 5 x + y + z = 3 of linear equations using Cramers rule. 2. (Chow A2.2, p. 540) Evaluate the determinants D(a) := 12 , 43 518 D(b) := 15 3 6 10 4 2 and D(c) := cos sin ,...

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(PHZ) Physics 3113 Mathematical Physics Florida Atlantic University Fall, 2009 Review Problems II Recommended Reading: Chow, Appendix 2; Boas, Sections 3.13.3. 1. (Chow A2.1, p. 540) Solve the system 2x y + 2z = 2 x + 10y 3z = 5 x + y + z = 3 of linear equations using Cramers rule. 2. (Chow A2.2, p. 540) Evaluate the determinants D(a) := 12 , 43 518 D(b) := 15 3 6 10 4 2 and D(c) := cos sin , sin cos where in the third case is an arbitrary real number. 3. (Chow A2.3, p. 542) Expand the second-order determinant D := ab cd using the Laplace development on each of the four rows and columns in the matrix. Show explicitly that one nds the same overall value in each case. 4. A2.4, (Chow p. 542) Evaluate the determinant 1 30 D := 2 6 4 1 0 2 using Laplace developments on the rst row and on the rst column. Show that you get the same result in each case. 5. (Boas 3.3.7) Use the seven rules for determinants enumerated in Chows book to show that 1a a2 1 a a2 1 a bc 2 = (c a)(b a)(c b) 0 1 b + a = (c a)(b a)(c b). D := 1 b ac = 1 b b 00 1 1 c c2 1 c ab Do not simply evaluate the determinants in this problem. The point is to practice using the rules while establishing each equality above. 6. (Boas 3.3.10) A square matrix A is called skew-symmetric if its components obey Aij = Aji . Show that the determinant of a skew-symetric matrix of odd order must vanish.
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FAU - PHZ - 3113
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