Business Math (11th Edition)
11th Edition
ISBN: 9780134496436
Author: Cheryl Cleaves, Margie Hobbs, Jeffrey Noble
Publisher: PEARSON
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Chapter 11, Problem 6CT
To determine
To prove: The formula
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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
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Chapter 11 Solutions
Business Math (11th Edition)
Ch. 11.1 - Prob. 1-1SCCh. 11.1 - Prob. 1-2SCCh. 11.1 - Prob. 1-3SCCh. 11.1 - Prob. 1-4SCCh. 11.1 - Prob. 2-1SCCh. 11.1 - Prob. 2-2SCCh. 11.1 - Prob. 2-3SCCh. 11.1 - Prob. 2-4SCCh. 11.1 - Prob. 3-1SCCh. 11.1 - Prob. 3-2SC
Ch. 11.1 - Prob. 3-3SCCh. 11.1 - Prob. 3-4SCCh. 11.1 - Prob. 4-1SCCh. 11.1 - Prob. 4-2SCCh. 11.1 - Prob. 4-3SCCh. 11.1 - Prob. 4-4SCCh. 11.1 - Prob. 1SECh. 11.1 - Prob. 2SECh. 11.1 - Prob. 3SECh. 11.1 - Prob. 4SECh. 11.1 - Prob. 5SECh. 11.1 - Prob. 6SECh. 11.1 - Prob. 7SECh. 11.1 - Prob. 8SECh. 11.1 - Prob. 9SECh. 11.1 - Prob. 10SECh. 11.1 - Prob. 11SECh. 11.1 - Prob. 12SECh. 11.1 - Prob. 13SECh. 11.1 - Prob. 14SECh. 11.1 - Prob. 15SECh. 11.1 - Prob. 16SECh. 11.2 - Prob. 1-1SCCh. 11.2 - Prob. 1-2SCCh. 11.2 - Prob. 1-3SCCh. 11.2 - Prob. 1-4SCCh. 11.2 - Prob. 2-1SCCh. 11.2 - Prob. 2-2SCCh. 11.2 - Prob. 2-3SCCh. 11.2 - Prob. 2-4SCCh. 11.2 - Prob. 3-1SCCh. 11.2 - Prob. 3-2SCCh. 11.2 - Prob. 3-3SCCh. 11.2 - Prob. 3-4SCCh. 11.2 - Prob. 3-5SCCh. 11.2 - Prob. 4-1SCCh. 11.2 - Prob. 4-2SCCh. 11.2 - Prob. 4-3SCCh. 11.2 - Prob. 4-4SCCh. 11.2 - Prob. 1SECh. 11.2 - Prob. 2SECh. 11.2 - Prob. 3SECh. 11.2 - Prob. 4SECh. 11.2 - Prob. 5SECh. 11.2 - Prob. 6SECh. 11.2 - Prob. 7SECh. 11.2 - Prob. 8SECh. 11.2 - Prob. 9SECh. 11.2 - Prob. 10SECh. 11.2 - Prob. 11SECh. 11.2 - Prob. 12SECh. 11.2 - Prob. 13SECh. 11.2 - Prob. 14SECh. 11.2 - Prob. 15SECh. 11.3 - Prob. 1-1SCCh. 11.3 - Prob. 1-2SCCh. 11.3 - Prob. 1-3SCCh. 11.3 - Prob. 1-4SCCh. 11.3 - Prob. 2-1SCCh. 11.3 - Prob. 2-2SCCh. 11.3 - Prob. 2-3SCCh. 11.3 - Prob. 2-4SCCh. 11.3 - Prob. 3-1SCCh. 11.3 - Prob. 3-2SCCh. 11.3 - Prob. 3-3SCCh. 11.3 - Prob. 3-4SCCh. 11.3 - Prob. 1SECh. 11.3 - Prob. 2SECh. 11.3 - Prob. 3SECh. 11.3 - Prob. 4SECh. 11.3 - Prob. 5SECh. 11.3 - Prob. 6SECh. 11.3 - Prob. 7SECh. 11.3 - Prob. 8SECh. 11.3 - Prob. 9SECh. 11.3 - Prob. 10SECh. 11.3 - Prob. 11SECh. 11 - Prob. 1ESCh. 11 - Prob. 2ESCh. 11 - Prob. 3ESCh. 11 - Prob. 4ESCh. 11 - Prob. 5ESCh. 11 - Prob. 6ESCh. 11 - Prob. 7ESCh. 11 - Prob. 8ESCh. 11 - Prob. 9ESCh. 11 - Prob. 10ESCh. 11 - Prob. 11ESCh. 11 - Prob. 12ESCh. 11 - Prob. 13ESCh. 11 - Prob. 14ESCh. 11 - Prob. 15ESCh. 11 - Prob. 16ESCh. 11 - Prob. 17ESCh. 11 - Prob. 18ESCh. 11 - Prob. 19ESCh. 11 - Prob. 20ESCh. 11 - Prob. 21ESCh. 11 - Prob. 22ESCh. 11 - Prob. 23ESCh. 11 - Prob. 24ESCh. 11 - Prob. 25ESCh. 11 - Prob. 26ESCh. 11 - Prob. 27ESCh. 11 - Prob. 28ESCh. 11 - Prob. 29ESCh. 11 - Prob. 30ESCh. 11 - Prob. 31ESCh. 11 - Prob. 32ESCh. 11 - Prob. 33ESCh. 11 - Prob. 34ESCh. 11 - Prob. 35ESCh. 11 - Prob. 36ESCh. 11 - Prob. 37ESCh. 11 - Prob. 38ESCh. 11 - Prob. 39ESCh. 11 - Prob. 40ESCh. 11 - Prob. 41ESCh. 11 - Prob. 42ESCh. 11 - Prob. 43ESCh. 11 - Prob. 44ESCh. 11 - Prob. 45ESCh. 11 - Prob. 46ESCh. 11 - Prob. 47ESCh. 11 - Prob. 48ESCh. 11 - Prob. 49ESCh. 11 - Prob. 50ESCh. 11 - Prob. 51ESCh. 11 - Prob. 52ESCh. 11 - Prob. 53ESCh. 11 - Prob. 54ESCh. 11 - Prob. 1PTCh. 11 - Prob. 2PTCh. 11 - Prob. 3PTCh. 11 - Prob. 4PTCh. 11 - Prob. 5PTCh. 11 - Prob. 6PTCh. 11 - Prob. 7PTCh. 11 - Prob. 8PTCh. 11 - Prob. 9PTCh. 11 - Prob. 10PTCh. 11 - Prob. 11PTCh. 11 - Prob. 12PTCh. 11 - Prob. 13PTCh. 11 - Prob. 14PTCh. 11 - Prob. 15PTCh. 11 - Prob. 16PTCh. 11 - Prob. 17PTCh. 11 - Prob. 18PTCh. 11 - Prob. 19PTCh. 11 - Prob. 20PTCh. 11 - Prob. 21PTCh. 11 - Prob. 22PTCh. 11 - Prob. 1CTCh. 11 - Prob. 2CTCh. 11 - Prob. 3CTCh. 11 - Prob. 4CTCh. 11 - Prob. 5CTCh. 11 - Prob. 6CTCh. 11 - Prob. 7CTCh. 11 - Prob. 8CTCh. 11 - Prob. 1CPCh. 11 - Prob. 2CPCh. 11 - Prob. 3CPCh. 11 - Prob. 4CPCh. 11 - Prob. 1CS1Ch. 11 - Prob. 2CS1Ch. 11 - Prob. 3CS1Ch. 11 - Prob. 4CS1Ch. 11 - Prob. 1CS2Ch. 11 - Prob. 2CS2Ch. 11 - Prob. 3CS2Ch. 11 - Prob. 4CS2Ch. 11 - Prob. 1CS3Ch. 11 - Prob. 2CS3Ch. 11 - Prob. 3CS3Ch. 11 - Prob. 4CS3
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