Math 205A Quiz 4, page 1 October 12, 2007 NAME
1. Let A=
5−61
2−47
102
−234
and B=
10 −20 30 −10
5 10 20 30
15 −10 10 10
. Find each of the following. If a particular
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.
1D) The entry in the second row, third column of AT+B.
2. What is the inverse of wx
yz
, and what condition(s) must w,x,yand zsatisfy in order for the
inverse to exist?
3. Suppose Aand Bare both n×nmatrices. Find a formula for the inverse of (AB)Tin terms of A−1
and B−1. Show all your steps.
4. Suppose the inverse of Ais
13 5
24 6
10 0 20
.
4A) Find all solutions of Ax=
1
0
4
4B) Do the columns of Aspan R3? Explain.