Text: Mathematics-Topics on Applied Math I, by S. Leon & S. Colley

**Section 1.1 -- p. 10:**# 6e, 6h, 7, 8(Use reduced row echelon form from Sec 1.2 instead of back substitution.), 9**Section 1.2 -- p. 23:**# 5a, 5e, 5f, 5i, 5j, 6b, 7, 8, 10**Section 1.3 -- p. 42:**# 1d, 1e, 1f, 1g, 1h, 2, 3, 4b, 8, 9, 10ab,

**Section 1.4 -- p. 56:**# 1, 4, 5, 6, 11acd, 13c, 16, 17, 20, 23, 24c, 27**Section 1.5 -- p. 66:**(See the bottom of p 62 through the top of p 64.) #10b, 10c, 10f, 10g, 9, 12a, 12d,**Section 1.2 -- p. 23:**# 15, 19, 22c

**Section 2.1 -- p. 94:**# 3b, 3f,__3h__, 4bcd, 6, 9, 11**Section 2.2 -- p. 101:**#__2__, 4, 6, 7,__10__, 12**Section 2.3 -- p. 109:**#__1c__, 2b, 5, 9

**Section 3.1 -- p. 122:**# 5, 8,__9__, 11,__12__, 14**Section 3.2 -- p. 131:**# 1, 3bcdef, 4ab,__5bc__, 6abc, 6de,__8__,__13__, 14, 16, 19,__22__**Section 3.3 -- p. 143:**#__2bce__,__3bce__, 5, 7,__8ac__, 16, 17

**Section 3.4 -- p. 149:**# 2bce,__5__, 9, 11, 12,__13__, 16**Section 3.5 -- p. 159:**# 1ab, 3ab,__5__,__9__(and express \(3x + 2\) in the \([2x - 1, 2x + 1]\) basis.)**Section 3.6 -- p. 165:**# 1b,__3__, 4ad,__8__,__13__,__18__, 22a, 26

**Section 4.1 -- p. 182:**# 1, 4(HINT: Write \((7,5)\) as a linear combination of \((1,2)\) and \((1,-1)\).), 5, 8, 11,__13__, 17,__19__,__21__,__22__, 23, 25**Section 4.2 -- p. 195:**# 4, 6,__8__, 13,__14__,__18__(HINT: First find the matrix relative to the standard bases for \(\mathbb{R}^3\) and \(\mathbb{R}^2\). Then multiply on the left and right by appropriate change of basis matrices.), 20**Section 4.3 -- p. 202:**# 2ab, 3, 5abc,__6__, 7, 9, 11, 13,__15__(HINT: Use the formulas: \(\displaystyle tr(A) = \sum_{i=1}^{n} A_{ii}\) and \(\displaystyle (AB)_{ij} = \sum_{k=1}^{n} A_{ik} B_{kj}\).)

**Section 5.1 -- p. 224:**# 1bd, 2bd, 3bd,__13__,__17__,__18__**Section 5.2 -- p. 233:**# 2,__4__, 6**Section 5.4 -- p. 251:**# 3,__7ac__,__8__, 10, 11,__16__,__26__,__9__(HINT: There is a trig identity for \(\sin A \cos B\) in terms of \(\sin(A+B)\) and \(\sin(A-B)\).)**Section 5.5 -- p. 269:**#__2__,__3__, 4, 6,__9__,__12__,__14__, 33, 34**Section 5.6 -- p. 280:**#__3__, 4,__Extra__: Find an orthonormal basis for \(P_3\) with the inner product \( \langle p,q\rangle = \int_0^1 x\, p(x) q(x) dx\) by applying the Gram-Schmidt procedure to \(1, x, x^2\).

**Section 6.1 -- p. 308:**#__1acdghijl__(Please list your eigenvalues in ascending order.), 3,__4__, 7, 9, 10,__14__, 28, 33**Section 6.3 -- p. 336:**#__1abcde__(Please list your eigenvalues in ascending order.),__2abcde__,__3abcde__(if invertible),__4__(Do b before a.), 5,__18__(Also: How are the eigenvalues and eigenvectors of B expressed in terms of those for A?),__29__

Last modified by pby on Apr 1,2013.