Homework 26-30 and pg 151 Problems
Dominique Dec
October 5, 2014
HW #26 b) Show that H =Spancfw_x1 , x2 mx3 is a subspace of R3
i) x1 = 0, x2 = 0, x3 = 0
H = cfw_0, 0, 0 (0, 0, 0) H.
ii) u : cfw_s1 v1 + s2 v2 + s3 v3 H
v : cfw_t1 v1 + t2 v2 + t3 v3
u +
Homework Week 12 #45-48 and Book
Dominique Dec
November 16, 2014
3a c
b 3c
; a, b, c in R be a subspace of R4 . 1) Find a basis for the subspace,
HW #45 Let H =
7a + 6b + 5c
3a + c
2) State the dimension.
1
0
3
c
0b
3a
3
1
0
0a b 3c
7a
Homework Week 9 and Book Work
Dominique Dec
October 26, 2014
w1
v1
u1
w2
v2
u2
HW #35 Show that Rn is a vector space: u = . , v = . , w = .
.
.
.
.
.
.
u1 + v1
v1
u1
u2 v2 u2 + v2
V : . + . =
.
.
. .
.
.
.
wn
vn
un
1. u + v
Rn
Homework for Week 7 with book work
Dominique Dec
October 11, 2014
4 0 0 0
7 1 0 0
#12 pg 168 Use codeterminants and cofactors to nd det
2 6 3 0
5 8 4 3
- 4(11+1 ) det [A1,1 ] = 4(1)(3)(3) = 36
6 3
2 4 0
9 0 4 1 0
#14 pg 168 Use codeterminants and cofacto
Homework #14-18, and book problems
Dominique Dec
September 20, 2014
#16 pg 60 Determine by inspection whether the vecors are linearly independent. Justify the answer.
2
3
2 , 6
8
12
No, vectors are linearly dependent because v2 is 3 v2 .
2
#18 pg 60 De
Homework 5, 6, 7, and 8 with extra Problems
Dominique Dec
September 3, 2014
#2 pg. 22 Determine which matrices are in reduced echelon form and which others are only in echelon
form.
a
b
c
d
reduced row echelon form
echelon form
reduced row echelon form
re
Homework 9, 10, 11, 12, 13 and Book Problems
Dominique Dec
September 10, 2014
#12 pg 40 Write the augmented matrix for the linear system that corresponds to the matrix
equation Ax = b. Then solve the system and write the solution as a vector.
1 2 1 1
1
2
Homework 1,2,3, and 4 with extra Problems
Dominique Dec
August 25, 2014
Homework #1 Show that (1, 1, 2) is a solution for the system of linear equations:
x1 2x2 + 3x3 =9
x1 + 3x2 =4
f (x) =
2x1 5x2 + 5x3 =17
1. 1 2(1) + 3(2) = 9
1 + 2 + 6 = 9 T rue
2. (1