# MATH 311 Sec 501 Spring 2013: Homework

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

## Homework 1

Due Wed 1/30
• 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,

## Homework 2

Due Fri 2/1
• 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

## Homework 3

Due Fri 2/8 (Underlined are the most important.)
• 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

## Homework 4

Due Wed 2/13 (Underlined are the most important.)
• 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

## Homework 5

Due Mon 2/18 (Underlined are the most important.)
• 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

## Homework 6

Due Fri 3/8 (Underlined are the most important.)
• 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 $$\displaystyle (AB)_{ij} = \sum_{k=1}^{n} A_{ik} B_{kj}$$.)

## Homework 7

Due Fri 3/22 (Underlined are the most important.)
• 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 $$1, x, x^2$$.

## Homework 8

Due Fri 4/5 (Underlined are the most important.)
• 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