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Number of Entries - Linear Algebra - Quiz, Exercises of Linear Algebra

This is the Quiz of Linear Algebra which includes Satisfies the Conditions, Information, Explicit Conditions, Guarantee, Conditions, Basis, Linear Combination, Basis Vectors, Column Vector, Bottom Entry etc. Key important points are: Number of Entries, Values, Give the Reason, Product, Entry, Matrix Product, Size, Method, Answer, Statements

Typology: Exercises

2012/2013

Uploaded on 02/27/2013

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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
2515
and let b=
94
228
63
.
2a. Find A1on your calculator using any method you like. Give your answer in fractions!
2b. Solve Ax=b.Give your answer in fractions!
3. Let AMn×n. Give four statements which are equivalent to the statement Ais invertible”. (From
the invertible matrix theorem). Note that A1exists” 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.

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Math 205A Quiz 04 page 1 October 13, 2008 NAME

  1. Let C =

3 7 w 2 9 5 1 3 0 2 4 6

 (^) let D =

. 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)T^ h. The size of the matrix product C CT^.

i. The 2-1 entry of DT^ D. j. The 1-2 entry of DT^ D.

  1. Let A =

 (^) and let b =

2a. Find A−^1 on your calculator using any method you like. Give your answer in fractions!

2b. Solve Ax = b. Give your answer in fractions!

  1. Let A ∈ Mn×n. Give four statements which are equivalent to the statement “A is invertible”. (From the invertible matrix theorem). Note that “A−^1 exists” 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.