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 vector orthogonal to W .
1
2
4/3
1/3
1
1
= 2/3
=
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 diagonalizable since it is a 3 3 matrix with 3 distinct eigenvalu
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 your answer.
1
2
1
(a) 1 , 1 , 3
0
1
4
1
2 1
1
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.
1 0
0 1
0 0
0 0
Using the standard basis B =
,
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 direction of flow in each branch is indicated, and the flo
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 vectors onto the first coordinate (i.e. the x-axis). Let