Math 205A Quiz 04 page 1 October 13, 2008 NAME
1. Let C=
37w2
95 13
02 46
let D=
83
15
20
011
. Suppose the 1-1 entry of the product CD is 51.
Find each of the following values. If the value doesn’t exist write “DNE” in the box, and give the reason.
a. The number of entries in CD.b. The 2-1 entry of CD.
c. The 4-3 entry of CD.d. The value of w.
e. The 3-2 entry of CT.f. The 2-3 entry of (DC)T
g. The 2-3 entry of (CD)Th. The size of the matrix product CC
T.
i. The 2-1 entry of DTD.j. The 1-2 entry of DTD.
2. Let A=
4 22 16
10 58 51
−2−515
and let b=
94
228
−63
.
2a. Find A−1on your calculator using any method you like. Give your answer in fractions!
2b. Solve Ax=b.Give your answer in fractions!
3. Let A∈Mn×n. Give four statements which are equivalent to the statement “Ais invertible”. (From
the invertible matrix theorem). Note that “A−1exists” is not one of them.
Hints: span, linearly independent, RREF, solutions of Ax=0, pivot, solutions of Ax=b, associated
linear transformation, . . . .
3a.
3b.
3c.
3d.