Intermediate Algebra (8th Edition)
8th Edition
ISBN: 9780134178967
Author: John Tobey Jr., Jeffrey Slater, Jamie Blair, Jenny Crawford
Publisher: PEARSON
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Chapter 4.1, Problem 28E
Find the solution to each system by the addition (elimination) method.
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Într-un bloc sunt apartamente cu 2 camere și apartamente cu 3 camere , în total 20 de apartamente și 45 de camere.Calculați câte apartamente sunt cu 2 camere și câte apartamente sunt cu 3 camere.
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]
Chapter 4 Solutions
Intermediate Algebra (8th Edition)
Ch. 4.1 - Verbal and Writing Skills, Exercises 1-4 Explain...Ch. 4.1 - Verbal and Writing Skills, Exercises 1-4 Explain...Ch. 4.1 - Verbal and Writing Skills, Exercises 1-4
3. How...Ch. 4.1 - Verbal and Writing Skills, Exercises 1-4 When you...Ch. 4.1 - Determine whether the given ordered pair is a...Ch. 4.1 - Prob. 6ECh. 4.1 - Solve the system of equations by graphing. Check...Ch. 4.1 - Prob. 8ECh. 4.1 - Solve the system of equations by graphing. Check...Ch. 4.1 - Solve the system of equations by graphing Check...
Ch. 4.1 - Solve the system of equations by graphing. Check...Ch. 4.1 - Solve the system of equations by graphing. Check...Ch. 4.1 - Solve the system of equations by graphing. Check...Ch. 4.1 - Solve the system of equations by graphing. Check...Ch. 4.1 - Find the solution to each system by the...Ch. 4.1 - Find the solution to each system by the...Ch. 4.1 - Find the solution to each system by the...Ch. 4.1 - Prob. 18ECh. 4.1 - Find the solution to each system by the...Ch. 4.1 - Prob. 20ECh. 4.1 - Find the solution to each system by the...Ch. 4.1 - Find the solution to each system by the...Ch. 4.1 - Find the solution to each system by the addition...Ch. 4.1 - Prob. 24ECh. 4.1 - Find the solution to each system by the addition...Ch. 4.1 - Prob. 26ECh. 4.1 - Find the solution to each system by the addition...Ch. 4.1 - Find the solution to each system by the addition...Ch. 4.1 - Find the solution to each system by the addition...Ch. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - If possible, solve each system of equations. Use...Ch. 4.1 - If possible, solve each system of equations. Use...Ch. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - If possible, solve each system of equations. Use...Ch. 4.1 - If possible, solve each system of equations. Use...Ch. 4.1 - Prob. 39ECh. 4.1 - If possible, solve each system of equations. Use...Ch. 4.1 - If possible, solve each system of equations. Use...Ch. 4.1 - If possible, solve each system of equations. Use...Ch. 4.1 - If possible, solve each system of equations. Use...Ch. 4.1 - If possible, solve each system of equations. Use...Ch. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - If possible, solve each system of equations. Use...Ch. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 1QQCh. 4.1 - Prob. 2QQCh. 4.1 - Prob. 3QQCh. 4.1 - Prob. 4QQCh. 4.2 - 1. Determine whether (2, 1, —4) is a solution to...Ch. 4.2 - Determine whether ( − 2 , 3 , 0 ) is a solution to...Ch. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Solve each system. 2 x + 2 z = − 7 + 3 y 3 2 x + y...Ch. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Solve each system. − 0.1 a + 0.2 b + 0.3 c = 0.1...Ch. 4.2 - Prob. 17ECh. 4.2 - Find the solution for each system of equations....Ch. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 1QQCh. 4.2 - Prob. 2QQCh. 4.2 - Prob. 3QQCh. 4.2 - Prob. 4QQCh. 4.3 - Use a system of two linear equations to solve...Ch. 4.3 - Use a system of two linear equations to solve...Ch. 4.3 - Use a system of two linear equations to solve...Ch. 4.3 - Use a system of two linear equations to solve...Ch. 4.3 - Use a system of two linear equations to solve...Ch. 4.3 - Use a system of two linear equations to solve...Ch. 4.3 - Use a system of two linear equations to solve...Ch. 4.3 - Prob. 8ECh. 4.3 - Use a system of two linear equations to solve...Ch. 4.3 - Prob. 10ECh. 4.3 - Use a system of two linear equations to solve...Ch. 4.3 - Prob. 12ECh. 4.3 - Use a system of two linear equations to solve...Ch. 4.3 - Use a system of two linear equations to solve...Ch. 4.3 - Use a system of two linear equations to solve...Ch. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Use a system of two linear equations to solve...Ch. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - Prob. 31ECh. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 1QQCh. 4.3 - Prob. 2QQCh. 4.3 - Prob. 3QQCh. 4.3 - Prob. 4QQCh. 4.4 - Verbal and Writing Skills, Exercises 1-4 In the...Ch. 4.4 - Prob. 2ECh. 4.4 - Verbal and Writing Skills, Exercises 1-4 Stephanie...Ch. 4.4 - Verbal and Writing Skills, Exercises 1-4 John...Ch. 4.4 - Graph the solution of each of the following...Ch. 4.4 - Graph the solution of each of the following...Ch. 4.4 - Graph the solution of each of the following...Ch. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Graph the solution of each of the following...Ch. 4.4 - Graph the solution of each of the following...Ch. 4.4 - Graph the solution of each of the following...Ch. 4.4 - Prob. 14ECh. 4.4 - Graph the solution of each of the following...Ch. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Graph the solution of each of the following...Ch. 4.4 - Prob. 20ECh. 4.4 - Graph the solution of the following systems of...Ch. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Graph the solution of the following systems of...Ch. 4.4 - Prob. 25ECh. 4.4 - Graph the solution of the following systems of...Ch. 4.4 - Graph the region determined by each of the...Ch. 4.4 - Prob. 28ECh. 4.4 - Hint: In exercises 29 and 30, it the coordinates...Ch. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Prob. 34ECh. 4.4 - Prob. 1QQCh. 4.4 - Prob. 2QQCh. 4.4 - Prob. 3QQCh. 4.4 - Prob. 4QQCh. 4 - Solve the following systems by graphing.
1.
Ch. 4 - Prob. 2RPCh. 4 - Solve the following systems by substitution.
3.
Ch. 4 - Prob. 4RPCh. 4 - Prob. 5RPCh. 4 - Prob. 6RPCh. 4 - Solve the following systems by addition. 7 x − 4 y...Ch. 4 - Prob. 8RPCh. 4 - Prob. 9RPCh. 4 - Prob. 10RPCh. 4 - Prob. 11RPCh. 4 - Prob. 12RPCh. 4 - Prob. 13RPCh. 4 - Prob. 14RPCh. 4 - Prob. 15RPCh. 4 - Prob. 16RPCh. 4 - Prob. 17RPCh. 4 - Prob. 18RPCh. 4 - Prob. 19RPCh. 4 - Prob. 20RPCh. 4 - Prob. 21RPCh. 4 - Prob. 22RPCh. 4 - Prob. 23RPCh. 4 - Prob. 24RPCh. 4 - Prob. 25RPCh. 4 - Prob. 26RPCh. 4 - Prob. 27RPCh. 4 - Prob. 28RPCh. 4 - Prob. 29RPCh. 4 - Use a system of linear equations to solve each of...Ch. 4 - Solve by any appropriate method. x − y = 1 5 x + y...Ch. 4 - Prob. 32RPCh. 4 - Prob. 33RPCh. 4 - Prob. 34RPCh. 4 - Prob. 35RPCh. 4 - Prob. 36RPCh. 4 - Prob. 37RPCh. 4 - Prob. 38RPCh. 4 - Prob. 39RPCh. 4 - Prob. 40RPCh. 4 - Prob. 41RPCh. 4 - Prob. 42RPCh. 4 - Prob. 43RPCh. 4 - Prob. 44RPCh. 4 - Prob. 1TCh. 4 - Prob. 2TCh. 4 - Prob. 3TCh. 4 - Prob. 4TCh. 4 - Prob. 5TCh. 4 - Prob. 6TCh. 4 - Prob. 7TCh. 4 - Prob. 8TCh. 4 - Prob. 9TCh. 4 - Prob. 10TCh. 4 - Prob. 11TCh. 4 - Prob. 12TCh. 4 - Prob. 13TCh. 4 - Prob. 14T
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- 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]arrow_forwardQuestion 4 (a) The following matrices represent linear maps on R² with respect to an orthonormal basis: = [1/√5 2/√5 [2/√5 -1/√5] " [1/√5 2/√5] A = B = [2/√5 1/√5] 1 C = D = = = [ 1/3/5 2/35] 1/√5 2/√5 -2/√5 1/√5' For each of the matrices A, B, C, D, state whether it represents a self-adjoint linear map, an orthogonal linear map, both, or neither. (b) For the quadratic form q(x, y, z) = y² + 2xy +2yz over R, write down a linear change of variables to u, v, w such that q in these terms is in canonical form for Sylvester's Law of Inertia. [6] [4]arrow_forwardpart b pleasearrow_forward
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