Math331-01 Exam 2
2/26/14 Name:Me
1. (10pts)
2. (18pts)
3. (10pts)
4. (10pts)
5. (10pts)
6. (12pts) Show that the set H of all 2 3 matrices of the form
[
00
00
]
a
is a subspace of M23 .
b
[
]
000
letting a = b = 0 we have
=OH
000
[
][
][
]
00a
00c
0 0 a
13
A = 1 0
11
1
1
The columns of B =
0
0
2
1 0 0 1
1 , T (X ) = AX, A reduces to 0 1 0 1
2
001 2
102
1 2 3 1
2 1 2
0
1 1
are a basis B for R4 and B 1 = 0
1 1 1 1
1 1 1
011
1 1 1
0
102
1
2 2
1
The columns of C = 1 1 1 are a basis C for R3 and C 1 = 1
Math331-01 haQuiz 3 1/29/14 NameMe
T (X ) = AX
1 2
0 0
00
is a linear transformation from R5 to R3 and A reduces to
001
1 0 2
013
1. The solutions of AX = O (in parametric vector form) are:
x1 2x2 + x5 = 0
x1 = 2x2 x5
The rows of the reduced form of A rep
Math331-01 Quiz
41
NameMe
22
[
1. Find the two eigenvalues of A =
]
13
. A is similar to what diagonal matrix D?
12 1
1
3
= (1 )2 36 = 2 2 35 = ( 7)( + 5) = 0
12
1
[
]
70
has the two solutions = 7, 5. That makes A similar to D =
.
0 5
111
2. I bought this