LINEAR ALGEBRA MATH 332
WORKSHEET 11 (6.3-6.5)
NAME:
SECTION:
1
2
1
3
1. Let u1 = 2 , u2 = 1 , y = 2 , and v = 1 . Let W = Spancfw_u1 , u2 .
1
0
3
1
(a) Write y as the sum of a vector in W and a v
LINEAR ALGEBRA MATH 332
WORKSHEET 10 (5.3, 6.1, 6.2)
NAME:
SECTION:
3 0 2
2
1. Let A = 1 0
0 0
5
(a) The matrix A has eigenvalues 0, 3 and 5. Is A diagonalizable? Justify your answer.
A is diagonaliz
LINEAR ALGEBRA MATH 332
WORKSHEET 12 (7.1, 7.4, 7.5)
NAME:
SECTION:
2 4
2 .
1. Let A = 1
1
2
(a) Find the singular value decomposition of A.
2 4
2 1 1
6 12
1
2 =
First, AT A =
.
4
2
2
12
24
1
2
T
2
T
LINEAR ALGEBRA MATH 332
WORKSHEET 3 (1.7 & 1.8)
NAME:
SECTION:
1. For each of the collections below, determine whether the collection of vectors is linearly independent or
linearly dependent. Explain
LINEAR ALGEBRA MATH 332
WORKSHEET 7 (4.4, 4.5)
1. Let S =
1 1
0 0
NAME:
SECTION:
0 1
1 0
1 0
,
,
,
1 0
0 1
1 0
(a) Use coordinate vectors to show that S forms a basis for M22 . Explain your work
LINEAR ALGEBRA MATH 332
WORKSHEET 2 (1.5, 1.7, 1.8)
NAME:
SECTION:
1. A network consists of a set of points called junctions with lines called branches connecting some or all of
the junctions. The dir
LINEAR ALGEBRA MATH 332
WORKSHEET 4 (1.9, 2.1, & 2.2)
NAME:
SECTION:
1. Let R : R2 R2 be the linear transformation that scales a vector by 2. Let S : R2 R2 be the linear
transformation that projects v