Math 205a Quiz 4 Worksheet - Bates College - 2007
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1Math 205A
Quiz 4, page 1
October 12, 2007
NAME
5
6 1
10
20 30
10
2
4 7
. Find each of the following. If a particular
5
10 20
30
1. Let A =
and B =
1
0 2
15
10 10
10
2
3 4
item doesn’t exist, explain why not!
1A) The number of entries of BA.
1B) The number of entries of A + A + A.
1C) The entry in the second row, third column of AB.
T
1D) The entry in the second row, third column of A
+ B.
w x
2. What is the inverse of
, and what condition(s) must w, x, y and z satisfy in order for the
y z
inverse to exist?
T
1
3. Suppose A and B are both n × n matrices. Find a formula for the inverse of (AB)
in terms of A
1
and B
. Show all your steps.
1 3
5
.
4. Suppose the inverse of A is
2 4
6
10 0 20
1
4A) Find all solutions of Ax =
0
4
3
4B) Do the columns of A span R
? Explain.
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