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Homework 1
- Section 1.1 The Vector Space of m x n Matrices
- Read Section 1.1. Do the True/False questions (p. 16). Do Problems 1.1, 1.2.
- A Geogebra linear combination activity
- Homework: 1.8, 1.11, 1.12, 1.13, 1.14, 1.16, 1.18, 1.20, 1.26, 1.28, 1.32, 1.36
- Hand In: 1.12*, 1.20*
- 1.12*. Complete Problem 1.12 on Page 18, but with the vectors \[X_1 = [1,-2,1]^t,\ \mbox{and}\ X_2 = [-3,2,1]^t\ \mbox{in}\ \mathbb{R}^3.\]
- 1.20*. Complete Problem 1.20 on Page 19, but with the adjustments as follows:
- In Part (a) use the vector \([-1,1]^t\).
- In Part (b) use the set of vectors \(\{[-1,1]^t,[2,1]^t\}\).
- In Part (e) use the set of vectors \(\{[1,-2,1]^t,[-1,3,1]^t\}\).
- In Part (f) use the set of vectors \(\{[1,-2,1]^t,[0,1,2]^t\}\).
- In Part (g) use the set of vectors \(\{[-2,1,0]^t,[-4,2,0]^t\}\).
- Read Section 1.2. Do the True/False questions (p. 37). Do Problem 1.44.
- A Geogebra activity on Systems of Linear Equations
- Homework: 1.46, 1.48, 1.49, 1.50
- Hand In: 1.46(i)*, 1.50*
- 1.46(i)*. Complete Problem 1.46(i) on Page 38, but with the system \[\matrix{3x+2y&=&0\cr 2x+3y-z&=&-2\cr x-y+z&=&2\cr}\]
- 1.50*. Complete Problem 1.50 on Page 39, but replace the equations with \(y-2x=2, y+3x=7\) and \(2y+3x=a\), and replace the system correspondingly with \[\matrix{y-2x&=&2\cr y+3x&=&7\cr 2y+3x&=&a\cr}\]