Pearson eText for College Mathematics for Trades and Technologies -- Instant Access (Pearson+)
10th Edition
ISBN: 9780137400010
Author: Cheryl Cleaves, Margie Hobbs
Publisher: PEARSON+
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Chapter 14.2, Problem 16E
To determine
To simplify: The expression
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1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix
A.
= [{² 1]
A =
b) Verify that PT AP gives the correct diagonal form.
2
01
-2
3
2) Given the following matrices A =
-1
0
1] an
and B =
0
1
-3
2
find the following matrices:
a) (AB) b) (BA)T
3) Find the inverse of the following matrix A using Gauss-Jordan elimination or
adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I).
[1 1 1
A = 3 5 4
L3 6 5
4) Solve the following system of linear equations using any one of Cramer's Rule,
Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and
check the correctness of your answer.
4x-y-z=1
2x + 2y + 3z = 10
5x-2y-2z = -1
5) a) Describe the zero vector and the additive inverse of a vector in the vector
space, M3,3.
b) Determine if the following set S is a subspace of M3,3 with the standard
operations. Show all appropriate supporting work.
13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of
the following sets and the cardinal number of each set.
a) W° and n(W)
b) (VUW) and n((V U W)')
c) VUWUX and n(V U W UX)
d) vnWnX and n(V WnX)
9) Use the Venn Diagram given below to determine the number elements in each of the following sets.
a) n(A).
b) n(A° UBC).
U
B
oh
a
k
gy
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W
z r
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Chapter 14 Solutions
Pearson eText for College Mathematics for Trades and Technologies -- Instant Access (Pearson+)
Ch. 14.1 - Prob. 1LCCh. 14.1 - Prob. 2LCCh. 14.1 - Prob. 1ECh. 14.1 - Prob. 2ECh. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8E
Ch. 14.1 - Prob. 9ECh. 14.1 - Prob. 10ECh. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.1 - Prob. 16ECh. 14.1 - Prob. 17ECh. 14.1 - Prob. 18ECh. 14.1 - Prob. 19ECh. 14.1 - Prob. 20ECh. 14.1 - Prob. 21ECh. 14.1 - Prob. 22ECh. 14.1 - Prob. 23ECh. 14.1 - Prob. 24ECh. 14.2 - Prob. 1LCCh. 14.2 - Prob. 2LCCh. 14.2 - Prob. 1ECh. 14.2 - Prob. 2ECh. 14.2 - Prob. 3ECh. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 6ECh. 14.2 - Prob. 7ECh. 14.2 - Prob. 8ECh. 14.2 - Prob. 9ECh. 14.2 - Prob. 10ECh. 14.2 - Prob. 11ECh. 14.2 - Prob. 12ECh. 14.2 - Prob. 13ECh. 14.2 - Prob. 14ECh. 14.2 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - Prob. 17ECh. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Prob. 20ECh. 14.2 - Prob. 21ECh. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - Prob. 27ECh. 14.2 - Prob. 28ECh. 14.2 - Prob. 29ECh. 14.2 - Prob. 30ECh. 14.2 - Prob. 31ECh. 14.2 - Prob. 32ECh. 14.2 - Prob. 33ECh. 14.2 - Prob. 34ECh. 14.2 - Prob. 35ECh. 14.2 - Prob. 36ECh. 14.2 - Prob. 37ECh. 14.2 - Prob. 38ECh. 14.2 - Prob. 39ECh. 14.2 - Prob. 40ECh. 14.2 - Prob. 41ECh. 14.2 - Prob. 42ECh. 14.2 - Prob. 43ECh. 14.3 - Prob. 1LCCh. 14.3 - Prob. 2LCCh. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - Prob. 3ECh. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10ECh. 14.3 - Prob. 11ECh. 14.3 - Prob. 12ECh. 14.3 - Prob. 13ECh. 14.3 - Prob. 14ECh. 14.3 - Prob. 15ECh. 14.3 - Prob. 16ECh. 14.3 - Prob. 17ECh. 14.3 - Prob. 18ECh. 14.4 - Prob. 1LCCh. 14.4 - Prob. 1ECh. 14.4 - Prob. 2ECh. 14.4 - Prob. 3ECh. 14.4 - Prob. 4ECh. 14.4 - Prob. 5ECh. 14.4 - Prob. 6ECh. 14.4 - Prob. 7ECh. 14.4 - Prob. 8ECh. 14.4 - Prob. 9ECh. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Prob. 15ECh. 14.4 - Prob. 16ECh. 14.4 - Prob. 17ECh. 14.4 - Prob. 18ECh. 14.4 - Prob. 19ECh. 14.4 - Prob. 20ECh. 14.4 - Prob. 21ECh. 14.4 - Prob. 22ECh. 14.4 - Prob. 23ECh. 14.4 - Prob. 24ECh. 14.4 - Prob. 25ECh. 14.4 - Prob. 26ECh. 14.4 - Prob. 27ECh. 14.4 - Prob. 28ECh. 14.4 - Prob. 29ECh. 14 - Prob. 1RECh. 14 - Prob. 2RECh. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - Prob. 5RECh. 14 - Prob. 6RECh. 14 - Prob. 7RECh. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RECh. 14 - Prob. 12RECh. 14 - Prob. 13RECh. 14 - Prob. 14RECh. 14 - Prob. 15RECh. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - Prob. 19RECh. 14 - Prob. 20RECh. 14 - Prob. 21RECh. 14 - Prob. 22RECh. 14 - Prob. 23RECh. 14 - Prob. 24RECh. 14 - Prob. 25RECh. 14 - Prob. 26RECh. 14 - Prob. 27RECh. 14 - Prob. 28RECh. 14 - Prob. 29RECh. 14 - Prob. 30RECh. 14 - Prob. 31RECh. 14 - Prob. 32RECh. 14 - Prob. 33RECh. 14 - Prob. 34RECh. 14 - Prob. 35RECh. 14 - Prob. 36RECh. 14 - Prob. 37RECh. 14 - Prob. 38RECh. 14 - Prob. 39RECh. 14 - Prob. 40RECh. 14 - Prob. 41RECh. 14 - Prob. 42RECh. 14 - Prob. 43RECh. 14 - Prob. 44RECh. 14 - Prob. 45RECh. 14 - Prob. 46RECh. 14 - Prob. 47RECh. 14 - Prob. 48RECh. 14 - Prob. 49RECh. 14 - Prob. 50RECh. 14 - Prob. 51RECh. 14 - Prob. 52RECh. 14 - Prob. 53RECh. 14 - Prob. 54RECh. 14 - Prob. 55RECh. 14 - Prob. 56RECh. 14 - Prob. 57RECh. 14 - Prob. 58RECh. 14 - Prob. 59RECh. 14 - Prob. 60RECh. 14 - Prob. 61RECh. 14 - Prob. 62RECh. 14 - Prob. 63RECh. 14 - Prob. 64RECh. 14 - Prob. 65RECh. 14 - Prob. 66RECh. 14 - Prob. 67RECh. 14 - Prob. 68RECh. 14 - Prob. 69RECh. 14 - Prob. 70RECh. 14 - Prob. 71RECh. 14 - Prob. 72RECh. 14 - Prob. 73RECh. 14 - Prob. 74RECh. 14 - Prob. 75RECh. 14 - Prob. 76RECh. 14 - Prob. 77RECh. 14 - Prob. 78RECh. 14 - Prob. 79RECh. 14 - Prob. 80RECh. 14 - Prob. 81RECh. 14 - Prob. 82RECh. 14 - Prob. 83RECh. 14 - Prob. 84RECh. 14 - Prob. 85RECh. 14 - Prob. 86RECh. 14 - Prob. 87RECh. 14 - Prob. 88RECh. 14 - Prob. 89RECh. 14 - Prob. 90RECh. 14 - Prob. 91RECh. 14 - Prob. 1CACh. 14 - Prob. 2CACh. 14 - Prob. 3CACh. 14 - Prob. 4CACh. 14 - Prob. 5CACh. 14 - Prob. 6CACh. 14 - Prob. 7CACh. 14 - Prob. 8CACh. 14 - Prob. 9CACh. 14 - Prob. 10CACh. 14 - Prob. 1PTCh. 14 - Prob. 2PTCh. 14 - Prob. 3PTCh. 14 - Prob. 4PTCh. 14 - Prob. 5PTCh. 14 - Prob. 6PTCh. 14 - Prob. 7PTCh. 14 - Prob. 8PTCh. 14 - Prob. 9PTCh. 14 - Prob. 10PTCh. 14 - Prob. 11PTCh. 14 - Prob. 12PTCh. 14 - Prob. 13PTCh. 14 - Prob. 14PTCh. 14 - Prob. 15PTCh. 14 - Prob. 16PTCh. 14 - Prob. 17PTCh. 14 - Prob. 18PTCh. 14 - Prob. 19PTCh. 14 - Prob. 20PTCh. 14 - Prob. 21PTCh. 14 - Prob. 22PTCh. 14 - Prob. 23PTCh. 14 - Prob. 24PTCh. 14 - Prob. 25PTCh. 14 - Prob. 26PTCh. 14 - Prob. 27PTCh. 14 - Prob. 28PTCh. 14 - Prob. 29PTCh. 14 - Prob. 30PTCh. 14 - Prob. 31PTCh. 14 - Prob. 32PT
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