MATH 205A,B LINEAR ALGEBRA - PROF. P. WONG
EXAM II - MARCH 18, 2013
NAME:
Section:(Circle one)
A(1 : 10)
B(2 : 40)
Instruction: Read each question carefully. Explain ALL your work and give reasons to support
your answers.
Advice: DONT spend too much time
MATH 205: Quiz 1 Show your work.
Name:
1. Consider the following matrix in reduced row echelon form (RREF).
1
0
0
0
1
0
0
0
1
(a) If the above matrix is a coecient matrix for a system of equations, then what can you say
about the solution of the system? (
TEST 1
Math 205
10/7/13
Name:
KEY
by writing my name I swear by the honor code
Read all of the following information before starting the exam:
Show all work, clearly and in order if you want to get full credit (matrices can be reduced into
RREF with calc
Math 205 Quiz 2
Name: KEY
1. Consider the following augmented matrix (in ref) for a system of equations written [A|b].
2031
0 1 0 2
0000
(a) Write the solution to the system in Parametric Vector Form.
3 1
2
2
t 0 + 2 | t is any real number.
1
0
(b) Writ
Math 205 Quiz 5
Name:
1. What are the three requirements for a subset H of a vector space V to be a subspace?
(a) 0 must be in H .
(b) H is closed under addition. For any x, y in H , x + y must be in H too.
(c) H is closed under scalar multiplication. For
Math 205 Quiz 4
Name:
1. Let A be an m n matrix, B be an n p matrix, and C be an n m matrix where n = m = p.
(a) Circle the matrix multiplications that can be computed.
AB
BC
CB
1
2. Consider the matrix A = 0
0
CA
AT B
AC
AT C
BT C
0
0 .
1
2
4
4
(a) Find
Math 205 Quiz 3
Name:
1. Consider the linear transformation T (x1 , x2 , x3 ) = (x1 2x2 , x1 + x2 + x3 ).
(a) What is the domain of T ? R3
(b) What is the codomain of T ? R2
1
(c) What is the image of x = 2 ?
3
3
6
(d) Determine the matrix A such that T (