MyLab Math with Pearson eText -- Standalone Access Card -- for Prealgebra (6th Edition)
6th Edition
ISBN: 9780134763811
Author: Margaret L. Lial, Diana Hestwood
Publisher: PEARSON
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Chapter 3.4, Problem 7E
Solve each application problem using the six problem-solving steps you learned in this section. See Examples 1 and 2.
Jason paid eight times as much for his laptop computer as he did for his printer. He paid a total of
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1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set
Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k
components, where k is the greatest common divisor of {n, r,s}.
Question 3
over a field K.
In this question, MË(K) denotes the set of n × n matrices
(a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is
equivalent to A-¹? Justify your answer.
(b) Let B be given by
8
B = 0 7 7
0 -7 7
Working over the field F2 with 2 elements, compute the rank of B as an element
of M2(F2).
(c) Let
1
C
-1 1
[4]
[6]
and consider C as an element of M3(Q). Determine the minimal polynomial
mc(x) and hence, or otherwise, show that C can not be diagonalised.
[7]
(d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write
down all the eigenvalues. Show your working.
[8]
R denotes the field of real numbers, Q denotes the field of rationals, and
Fp denotes the field of p elements given by integers modulo p. You may refer to general
results from lectures.
Question 1
For each non-negative integer m, let R[x]m denote the
vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m.
x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent
(a) Let vi = x, V2 =
list in R[x] 3.
(b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4)
is a basis of R[x] 3.
[8]
[6]
(c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a
linear map.
[6]
(d) Write down the matrix for the map ƒ defined in (c) with respect to the basis
(2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3.
[5]
Chapter 3 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Prealgebra (6th Edition)
Ch. 3.1 - Find the perimeter of each square, using the...Ch. 3.1 - Prob. 2CPCh. 3.1 - Prob. 3CPCh. 3.1 - Prob. 4CPCh. 3.1 - Prob. 5CPCh. 3.1 - Find the perimeter of each triangle. a p=31mm++p=...Ch. 3.1 - Prob. 7CPCh. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3E
Ch. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Draw a sketch of each square and label the lengths...Ch. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10ECh. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.1 - In an equilateral triangle, all sides have the...Ch. 3.1 - Be sure that you have done Exercise 49 first. a...Ch. 3.1 - Prob. 51ECh. 3.1 - Prob. 52ECh. 3.1 - Prob. 53ECh. 3.1 - Prob. 54ECh. 3.2 - Prob. 1CPCh. 3.2 - Prob. 2CPCh. 3.2 - Prob. 3CPCh. 3.2 - Prob. 4CPCh. 3.2 - Prob. 5CPCh. 3.2 - Prob. 6CPCh. 3.2 - Prob. 7CPCh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Solve each application problem to find the...Ch. 3.2 - Prob. 48ECh. 3.2 - Prob. 49ECh. 3.2 - Prob. 50ECh. 3.2 - Prob. 51ECh. 3.2 - Use your knowledge of perimeter and area to work...Ch. 3.SE - Prob. 1SECh. 3.SE - Prob. 2SECh. 3.SE - Name each figure and find its perimeter and area...Ch. 3.SE - Prob. 4SECh. 3.SE - Prob. 5SECh. 3.SE - Prob. 6SECh. 3.SE - Prob. 7SECh. 3.SE - Name each figure and find its perimeter and area...Ch. 3.SE - Prob. 9SECh. 3.SE - Prob. 10SECh. 3.SE - Prob. 11SECh. 3.SE - Prob. 12SECh. 3.SE - Prob. 13SECh. 3.SE - Prob. 14SECh. 3.SE - Prob. 15SECh. 3.SE - Prob. 16SECh. 3.SE - Prob. 17SECh. 3.SE - Prob. 18SECh. 3.SE - Prob. 19SECh. 3.SE - Prob. 20SECh. 3.3 - Prob. 1CPCh. 3.3 - Prob. 2CPCh. 3.3 - Prob. 3CPCh. 3.3 - Prob. 4CPCh. 3.3 - Five donors each gave the same amount of money to...Ch. 3.3 - Prob. 6CPCh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Write an algebraic expression, using x as the...Ch. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Write an algebraic expression, using x as the...Ch. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Solve each application problem. Use the six...Ch. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Solve each application problem. Use the six...Ch. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - Prob. 42ECh. 3.3 - Solve each application problem. Use the six...Ch. 3.3 - Prob. 44ECh. 3.3 - Prob. 45ECh. 3.3 - Prob. 46ECh. 3.4 - Prob. 1CPCh. 3.4 - Prob. 2CPCh. 3.4 - Prob. 3CPCh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Solve each application problem using the six...Ch. 3.4 - Prob. 4ECh. 3.4 - Solve each application problem using the six...Ch. 3.4 - Prob. 6ECh. 3.4 - Solve each application problem using the six...Ch. 3.4 - Prob. 8ECh. 3.4 - Solve each application problem using the six...Ch. 3.4 - Prob. 10ECh. 3.4 - Solve each application problem using the six...Ch. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Solve each application problem using the six...Ch. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - In Exercises 17 22, use the formula for the...Ch. 3.4 - A photograph measures 8in. by 10in. Earl put it in...Ch. 3.4 - Prob. 24ECh. 3.TYW - Prob. 1TYWCh. 3.TYW - Prob. 2TYWCh. 3.TYW - Prob. 3TYWCh. 3.TYW - Prob. 4TYWCh. 3.TYW - Prob. 5TYWCh. 3.TYW - Prob. 6TYWCh. 3.CR - Prob. 1CRCh. 3.CR - Prob. 2CRCh. 3.CR - Prob. 3CRCh. 3.CR - Prob. 4CRCh. 3.CR - Prob. 5CRCh. 3.CR - Prob. 6CRCh. 3.CR - Prob. 7CRCh. 3.CR - In Exercises 8-10, draw a sketch of each shape...Ch. 3.CR - Prob. 9CRCh. 3.CR - Prob. 10CRCh. 3.CR - In Exercises 11-13, use the appropriate formula to...Ch. 3.CR - Prob. 12CRCh. 3.CR - Prob. 13CRCh. 3.CR - Write each phrase as an algebraic expression. Use...Ch. 3.CR - Prob. 15CRCh. 3.CR - Prob. 16CRCh. 3.CR - Prob. 17CRCh. 3.CR - Prob. 18CRCh. 3.CR - Prob. 19CRCh. 3.CR - Prob. 20CRCh. 3.CR - Prob. 21CRCh. 3.CR - Use the six problem-solving steps to solve each...Ch. 3.CR - Prob. 23CRCh. 3.CR - Use the six problem-solving steps to solve each...Ch. 3.CR - Prob. 25CRCh. 3.CR - Prob. 26CRCh. 3.MRE - Prob. 1MRECh. 3.MRE - Prob. 2MRECh. 3.MRE - Prob. 3MRECh. 3.MRE - Prob. 4MRECh. 3.MRE - Prob. 5MRECh. 3.MRE - Prob. 6MRECh. 3.MRE - Prob. 7MRECh. 3.MRE - Prob. 8MRECh. 3.MRE - Use the information in the advertisement and the...Ch. 3.MRE - Prob. 10MRECh. 3.CT - Prob. 1CTCh. 3.CT - Prob. 2CTCh. 3.CT - Prob. 3CTCh. 3.CT - Prob. 4CTCh. 3.CT - Prob. 5CTCh. 3.CT - Prob. 6CTCh. 3.CT - Prob. 7CTCh. 3.CT - Prob. 8CTCh. 3.CT - Prob. 9CTCh. 3.CT - Prob. 10CTCh. 3.CT - Prob. 11CTCh. 3.CT - Prob. 12CTCh. 3.CT - Prob. 13CTCh. 3.CT - Prob. 14CTCh. 3.CT - Prob. 15CTCh. 3.CT - Prob. 16CTCh. 3.CT - Prob. 17CTCh. 3.CT - Solve each application problem, using the six...Ch. 3.CT - Prob. 19CTCh. 3.CT - Prob. 20CTCh. 3.CT - Prob. 21CTCh. 3.CM - Prob. 1CMCh. 3.CM - Prob. 2CMCh. 3.CM - Prob. 3CMCh. 3.CM - Prob. 4CMCh. 3.CM - a Round 3795 to the nearest ten. b Round 493, 662...Ch. 3.CM - Prob. 6CMCh. 3.CM - Prob. 7CMCh. 3.CM - Prob. 8CMCh. 3.CM - Prob. 9CMCh. 3.CM - Prob. 10CMCh. 3.CM - Prob. 11CMCh. 3.CM - Prob. 12CMCh. 3.CM - Prob. 13CMCh. 3.CM - Prob. 14CMCh. 3.CM - Prob. 15CMCh. 3.CM - Prob. 16CMCh. 3.CM - Prob. 17CMCh. 3.CM - Prob. 18CMCh. 3.CM - Prob. 19CMCh. 3.CM - Prob. 20CMCh. 3.CM - Prob. 21CMCh. 3.CM - Prob. 22CMCh. 3.CM - Prob. 23CMCh. 3.CM - Prob. 24CMCh. 3.CM - Prob. 25CMCh. 3.CM - Prob. 26CMCh. 3.CM - Prob. 27CMCh. 3.CM - Prob. 28CMCh. 3.CM - Prob. 29CMCh. 3.CM - Find the perimeter and area of each shape. The...Ch. 3.CM - Prob. 31CMCh. 3.CM - Prob. 32CMCh. 3.CM - Prob. 33CMCh. 3.CM - Prob. 34CMCh. 3.CM - Prob. 35CMCh. 3.CM - Prob. 36CMCh. 3.CM - Prob. 37CMCh. 3.CM - Prob. 38CM
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