Introduction to Elementary Applied Linear Algebra & Differential Equations
MATH 242

Spring 2013
Homework Solutions
MATH 242
Mar 20, 2012
5.4 # 1a, 1b, 1c, 1d, 1e, 2, 3, 4, 5
5.4 # 1a. Solve the following initial value problems.
y + ty = t, y(0) = y0
Solution. This is separable and can be rewritten as
y
= t.
1y
Integrating gives
1
ln 1 y = t2 + C.
Introduction to Elementary Applied Linear Algebra & Differential Equations
MATH 242

Spring 2013
Homework Solutions
MATH 242
Feb 7, 2012
1.3 # 9, 10, 16, 17, 18
1.4 # 1, 2, 4, 5, 6
1.3 # 9. Find all solutions of z 3 + 8 = 0.
Solution. We rearrange the equation to z 3 = 8 and write 8 in its polar form: 8 = 8(cos()+
i sin(). The three solutions are as
Introduction to Elementary Applied Linear Algebra & Differential Equations
MATH 242

Spring 2013
Homework Solutions
MATH 242
Mar 6, 2012
3.3 # 1, 2, 3, 4, 5 (ignore the subspace questions for now), 6 (ignore the subspace questions for
now)
3.3 # 1. (a) Consider the vector space consisting of one vector 0 with addition and multiplication dened
by (i)
Introduction to Elementary Applied Linear Algebra & Differential Equations
MATH 242

Spring 2013
Homework Solutions
MATH 242
Feb 7, 2012
1.5 # 1, 2, 6, 8
1.6 # 1, 2, 3, 4, 5, 6, 7, 11, 12, 18, 19
1.5 # 1. Consider the function dened by f (z) = z 3 . What is its domain? Find its real and imaginary
parts. Where is it dierentiable? What is its derivativ
Introduction to Elementary Applied Linear Algebra & Differential Equations
MATH 242

Spring 2013
Homework Solutions
MATH 242
Mar 6, 2012
3.2 # 1, 2, 8, 9, 12
3.3 # 8, 9
3.4 # 5, 6, 7, 8
3.2 # 1 Let u = (1, 2, 1) and v = (3, 1, 4). Compute u + v, u v, 2u, 1 v, and u + 2v. Make
2
sketches of arrows representing each of these vectors.
Solution.
u + v =
Introduction to Elementary Applied Linear Algebra & Differential Equations
MATH 242

Spring 2013
Homework Solutions
MATH 242
Mar 20, 2012
4.2 # 1, 12, 15
4.3 # 3, 10
4.5 # 1, 2ab, 3 (omit diagonal representation), 4 (omit diagonal representation), 6, 7, 8, 9
4.2 # 1. Let U be R2 and V be R2 . Let f (u) be the reection of u in the x axis; that is, if