Worksheet #9 in Math 547. September 17th 2015
Name & Initials:
If U and V are subspaces of Rn show that
W = U + V := cfw_u + v|u U, v V
is a subspace of Rn
u1 , u2 , u3 forms a basis for a subspace U in R4
1
2
3
1
1
1
u1 =
1 , u2 = 1 , u3 = 1
Worksheet #6 in Math 547. September 3rd 2015
Name & Initials:
Let T (x) be the projection of (x, y) onto the vector (1, 3). Find the 2 2
matrix representation for T , i.e. T (x) = [T ]x
[T ] =
Worksheet #7 in Math 547. September 8th 2015
Name & Initials:
1 1
1
A = 1 0 2
2 1
4
Compute the lu factorization of A, i.e. a lower triangular matrix L and upper
triangular matrix U such that LU = A. Then use this to solve Ax = b where
b = [0, 1, 2]T .
Worksheet #8 in Math 547. September 15th 2015
Name & Initials:
Compute the LU factorization of
2
1 0 0
4
4 1 0
0
2
2 1
A=
0
0 6 4
0
0 0 2
0
0
0
1
3
Then use this to solve Ax = b where b = [4, 11, 4, 3, 7]T . Note, all numbers
are integers.
01/11/2016
Discrete Mathematics and its application 7th Ed by Kenneth Rosen,
McGraw Hill
Friday homeworks DONT MISS FRIDAY CLASS lulz
Natural numbers positive integers
C is a subset of or is contained in
Integers 0, +-1, +-2, .etc - Z/
Boldface Q rational
Completed
Economics 101
P. Conway, Fall 2014
In-class worksheet: Week 3, Class 1
1. A shortage is an excess of quantity demanded over quantity supplied at the
current price.
Despite the high unemployment rate at present, the newspapers report that
there i
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