Math 205b Quiz 04 Page 1 Matrix Worksheet
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1Quiz 04 page 1
10/16/2009
Math 205B
Name
c 3
1 a 2
1. Let A =
and B =
4 2
.
3 5
b
8 1
(1A) Find the matrix product AB.
(1B) Suppose the first two entries in the first row of this product are 0 and
1 respectively. Find c.
m n
1
2. Suppose A =
. What is A
? Under what conditions on m, n, s, t is A a singular matrix?
s
t
3. Suppose A is a 2x2 matrix which row-reduces to I
after the following row operations are applied in this order to A:
2
(step 1) Row 1 of A is replaced with (row 1 + 4 row 2).
(step 2) The second row of the resulting matrix is divided by 2.
(step 3) In the matrix resulting from step (2), the second row is replaced with (row 2 + 3 row 1).
(3A) What are the three elementary matrices E
, E
, E
corresponding to the three steps 1, 2 and 3, respectively?
1
2
3
=
=
=
E
E
E
1
2
3
1
(3B) The product of E
, E
, E
, in some order, gives A
. What is that order? (eg, “E
E
E
”?)
1
2
3
2
1
3
1
(3C) From (3B), what is A
?
(3D) What is A? Explain how you found it (there is more than one way to find it).
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