Homework 1: Chapter 1

Section 1: 2, 5 (c,d), 9

Section 2: 7, 9, 15.

Homework 2: Chapter 1

Section 3: 4 (a,b,c), 9 (a,b,c), 17

Section 4: 4, 9, 10 (a,c,e), 22, 33(a,b,c)

Section 5: 2, 5 (a,b,c), 7 (a,b), 11 (a,b), 19 (a,b)

Homework 3.

Chapter 1, Section 5: 9 (a,b), 10 (e,f)

Chapter 2, Section 1: 2 (a,b,c), 3 (a,d), 6

Let A be an 4 by 4 matrix with entries a_ij. In the expression of the determinant of A what is the sign of the product
a) a₁₂a₂₃a₃₄a₄₁ ?
b) a₁₄a₂₃a₃₂a₄₁ ?

Homework 4.

Chapter 2, Section 1: 1, 3 (g, h)

Section 2: 2 (a), 3 (e,f), 4, 7 (a,c), 10, 12 (a,b), 16.

Section 3: 2 (a, c), 5 (a,b),

Let A be the n by n matrix with 1's on the main diagonal, -1's in the diagonal above the main diagonal, 1's on the diagonal just below the main diagonal, and 0's everywhere else. Show that the determinant of A is a Fibonacci number.

Homework 5.

Chapter 3, Section 2: 3 (a-g), 4 (b,d), 5 (a,b,c,d), 10 (a,b), 12 (a,b,c), 13 (a,b)_

Section 3: 2 (a,c,e), 3 (a,c,e), 8 (a,b,c,d), 9 (a,b,c,d)

Section 4: 3 (a,b,c), 10, 11, 13

Homework 6.

Chapter 3.

Section 5: 2, 4, 6 (a,b), 7, 8

Section 6: 1 (a,b,c), 2 (a), 3 (a), 6, 9, 10, 15 (a,b), 16

Homework 7.

Find the matrix of the reflection of R³ about the plane x+y-z=0.

Find the matrix of the linear transformation of R² which is the composition of dilation by 2, rotation throught 30 degrees and reflection about the line y=2x.

Homework 8.

Chapter 4, Section 4: 3,4

Chapter 5, Section 1: 1 (a,b), 6, 7

Chaper 5. Section 2: 1 (a,b), 4,6

Homework 9.

Chapter 5, Section 1: 17 (a,b), 18, (a,b),

Section 3: 1 (a, b, c), 2 (a,b,c), 3 (a,c), 6

Section 4: 3 (a,b), 7 (a,b,c), 8 (a, b, b, c), 9, 11 (a,b,c), 16

Homework 10.

Chapter 5. Section 5: 1 (a,c,d), 2 (a,b), 8, 21 (a,b), 22 (a,b), 23 (a,b)

Sectiion 6: 3, 4, 7, 8

Homework 11.

Chapter 6. Section 1: 1 (a,c, e, g)

Section 3: 1 (a,b,c,d), 2 (a,b,c,d), 4 (a), 7, 8 (a,b,c), 23 (b,c)

Section 4: 2 (a,b), 4 (a,b,c,d), 5 (a,b,c)