Explanation Given information: The system of equations is as follows. 2 u − 3 v + 2 w = 7 3 u + v − 3 w = − 6 u + 4 v + w = − 13 Calculation: The system of equations in the form of A X = C . Provide the matrix A and C for the system of equations as shown below. A = [ 2 − 3 2 3 1 − 3 1 4 1 ] C = [ 7 − 6 − 13 ] Calculate the inverse of matrix A ( A − 1 ) using Gauss-Jordan elimination method as shown below. Transform [ A | I ] into [ I | A − 1 ] . Substitute [ 2 − 3 2 3 1 − 3 1 4 1 ] for A , [ 1 0 0 0 1 0 0 0 1 ] for I , and apply the row operations as follows. [ 2 − 3 2 3 1 − 3 1 4 1 | 1 0 0 0 1 0 0 0 1 ] = [ 1 − 3 2 1 3 1 − 3 1 4 1 | 1 2 0 0 0 1 0 0 0 1 ] R 1 → 1 2 R 1 = [ 1 − 3 2 1 0 11 2 − 6 0 11 2 0 | 1 2 0 0 − 3 2 1 0 − 1 2 0 1 ] R 2 → R 2 − 3 R 1 R 3 → R 3 − R 1 = [ 1 − 3 2 1 0 1 − 12 11 0 11 2 0 | 1 2 0 0 − 3 11 2 11 0 − 1 2 0 1 ] R 2 → 2 11 R 2 = [ 1 0 − 7 11 0 1 − 12 11 0 0 6 | 1 11 3 11 0 − 3 11 2 11 0 1 − 1 1 ] R 1 → R 1 + 3 2 R 2 R 3 → R 3 − 11 2 R</

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 16, Problem 35RE

To determine

Solve the system of equations using inverse of the coefficient matrix.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16, Problem 34RE

Chapter 16, Problem 36RE

Students have asked these similar questions

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]

Question 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]

part b please

Chapter 16 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

Ch. 16.1 - For matrices A and B, find A + B. Ch. 16.1 - Prob. 2PE Ch. 16.1 - Prob. 3PE Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E

Ch. 16.1 - Prob. 8E Ch. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 10E Ch. 16.1 - Prob. 11E Ch. 16.1 - Prob. 12E Ch. 16.1 - Prob. 13E Ch. 16.1 - Prob. 14E Ch. 16.1 - Prob. 15E Ch. 16.1 - Prob. 16E Ch. 16.1 - Prob. 17E Ch. 16.1 - Prob. 18E Ch. 16.1 - Prob. 19E Ch. 16.1 - Prob. 20E Ch. 16.1 - Prob. 21E Ch. 16.1 - Prob. 22E Ch. 16.1 - Prob. 23E Ch. 16.1 - Prob. 24E Ch. 16.1 - Prob. 25E Ch. 16.1 - Prob. 26E Ch. 16.1 - Prob. 27E Ch. 16.1 - Prob. 28E Ch. 16.1 - Prob. 29E Ch. 16.1 - Prob. 30E Ch. 16.1 - Prob. 31E Ch. 16.1 - Prob. 32E Ch. 16.1 - Prob. 33E Ch. 16.1 - Prob. 34E Ch. 16.1 - Prob. 35E Ch. 16.1 - Prob. 36E Ch. 16.1 - Prob. 37E Ch. 16.1 - Prob. 38E Ch. 16.1 - Prob. 39E Ch. 16.1 - Prob. 40E Ch. 16.1 - Prob. 41E Ch. 16.1 - Prob. 42E Ch. 16.1 - Prob. 43E Ch. 16.1 - Prob. 44E Ch. 16.2 - Prob. 1PE Ch. 16.2 - Prob. 2PE Ch. 16.2 - Prob. 3PE Ch. 16.2 - Prob. 1E Ch. 16.2 - Prob. 2E Ch. 16.2 - Prob. 3E Ch. 16.2 - Prob. 4E Ch. 16.2 - Prob. 5E Ch. 16.2 - Prob. 6E Ch. 16.2 - Prob. 7E Ch. 16.2 - Prob. 8E Ch. 16.2 - Prob. 9E Ch. 16.2 - Prob. 10E Ch. 16.2 - Prob. 11E Ch. 16.2 - Prob. 12E Ch. 16.2 - Prob. 13E Ch. 16.2 - Prob. 14E Ch. 16.2 - Prob. 15E Ch. 16.2 - Prob. 16E Ch. 16.2 - Prob. 17E Ch. 16.2 - Prob. 18E Ch. 16.2 - Prob. 19E Ch. 16.2 - Prob. 20E Ch. 16.2 - Prob. 21E Ch. 16.2 - Prob. 22E Ch. 16.2 - Prob. 23E Ch. 16.2 - Prob. 24E Ch. 16.2 - Prob. 25E Ch. 16.2 - Prob. 26E Ch. 16.2 - Prob. 27E Ch. 16.2 - Prob. 28E Ch. 16.2 - Prob. 29E Ch. 16.2 - Prob. 30E Ch. 16.2 - Prob. 31E Ch. 16.2 - Prob. 32E Ch. 16.2 - Prob. 33E Ch. 16.2 - Prob. 34E Ch. 16.2 - Prob. 35E Ch. 16.2 - Prob. 36E Ch. 16.2 - Prob. 37E Ch. 16.2 - Prob. 38E Ch. 16.2 - Prob. 39E Ch. 16.2 - Prob. 40E Ch. 16.2 - Prob. 41E Ch. 16.2 - Prob. 42E Ch. 16.2 - Prob. 43E Ch. 16.2 - Prob. 44E Ch. 16.2 - Prob. 45E Ch. 16.2 - Prob. 46E Ch. 16.2 - Prob. 47E Ch. 16.2 - Prob. 48E Ch. 16.3 - Prob. 1PE Ch. 16.3 - Prob. 2PE Ch. 16.3 - Prob. 1E Ch. 16.3 - Prob. 2E Ch. 16.3 - Prob. 3E Ch. 16.3 - Prob. 4E Ch. 16.3 - Prob. 5E Ch. 16.3 - Prob. 6E Ch. 16.3 - Prob. 7E Ch. 16.3 - Prob. 8E Ch. 16.3 - Prob. 9E Ch. 16.3 - Prob. 10E Ch. 16.3 - Prob. 11E Ch. 16.3 - Prob. 12E Ch. 16.3 - Prob. 13E Ch. 16.3 - Prob. 14E Ch. 16.3 - Prob. 15E Ch. 16.3 - Prob. 16E Ch. 16.3 - Prob. 17E Ch. 16.3 - Prob. 18E Ch. 16.3 - Prob. 19E Ch. 16.3 - In Exercises 11–20, find the inverse of each of...Ch. 16.3 - In Exercises 21–28, find the inverse of each of...Ch. 16.3 - In Exercises 21–28, find the inverse of each of...Ch. 16.3 - Prob. 23E Ch. 16.3 - Prob. 24E Ch. 16.3 - Prob. 25E Ch. 16.3 - Prob. 26E Ch. 16.3 - Prob. 27E Ch. 16.3 - Prob. 28E Ch. 16.3 - Prob. 29E Ch. 16.3 - Prob. 30E Ch. 16.3 - Prob. 31E Ch. 16.3 - Prob. 32E Ch. 16.3 - Prob. 33E Ch. 16.3 - Prob. 34E Ch. 16.3 - Prob. 35E Ch. 16.3 - Prob. 36E Ch. 16.3 - Prob. 37E Ch. 16.3 - Prob. 38E Ch. 16.3 - Prob. 39E Ch. 16.3 - Prob. 40E Ch. 16.3 - Prob. 41E Ch. 16.3 - In Exercises 35–44, solve the given problems. 42....Ch. 16.3 - Prob. 43E Ch. 16.3 - Prob. 44E Ch. 16.4 - Prob. 1PE Ch. 16.4 - Prob. 1E Ch. 16.4 - Prob. 2E Ch. 16.4 - Prob. 3E Ch. 16.4 - Prob. 4E Ch. 16.4 - Prob. 5E Ch. 16.4 - Prob. 6E Ch. 16.4 - Prob. 7E Ch. 16.4 - Prob. 8E Ch. 16.4 - Prob. 9E Ch. 16.4 - Prob. 10E Ch. 16.4 - Prob. 11E Ch. 16.4 - Prob. 12E Ch. 16.4 - Prob. 13E Ch. 16.4 - Prob. 14E Ch. 16.4 - Prob. 15E Ch. 16.4 - Prob. 16E Ch. 16.4 - Prob. 17E Ch. 16.4 - Prob. 18E Ch. 16.4 - Prob. 19E Ch. 16.4 - Prob. 20E Ch. 16.4 - Prob. 21E Ch. 16.4 - Prob. 22E Ch. 16.4 - Prob. 23E Ch. 16.4 - Prob. 24E Ch. 16.4 - Prob. 25E Ch. 16.4 - Prob. 26E Ch. 16.4 - Prob. 27E Ch. 16.4 - Prob. 28E Ch. 16.4 - Prob. 29E Ch. 16.4 - Prob. 30E Ch. 16.4 - In Exercises 29–40, solve the indicated systems of...Ch. 16.4 - Prob. 32E Ch. 16.4 - Prob. 33E Ch. 16.4 - Prob. 34E Ch. 16.4 - Prob. 35E Ch. 16.4 - Prob. 36E Ch. 16.4 - Prob. 37E Ch. 16.4 - Prob. 38E Ch. 16.4 - Prob. 39E Ch. 16.4 - Prob. 40E Ch. 16.5 - Prob. 1PE Ch. 16.5 - Prob. 1E Ch. 16.5 - Prob. 2E Ch. 16.5 - Prob. 3E Ch. 16.5 - Prob. 4E Ch. 16.5 - Prob. 5E Ch. 16.5 - Prob. 6E Ch. 16.5 - Prob. 7E Ch. 16.5 - Prob. 8E Ch. 16.5 - Prob. 9E Ch. 16.5 - Prob. 10E Ch. 16.5 - Prob. 11E Ch. 16.5 - Prob. 12E Ch. 16.5 - Prob. 13E Ch. 16.5 - Prob. 14E Ch. 16.5 - Prob. 15E Ch. 16.5 - Prob. 16E Ch. 16.5 - Prob. 17E Ch. 16.5 - Prob. 18E Ch. 16.5 - Prob. 19E Ch. 16.5 - Prob. 20E Ch. 16.5 - Prob. 21E Ch. 16.5 - Prob. 22E Ch. 16.5 - Prob. 23E Ch. 16.5 - Prob. 24E Ch. 16.5 - Prob. 25E Ch. 16.5 - Prob. 26E Ch. 16.5 - Prob. 27E Ch. 16.5 - Prob. 28E Ch. 16.5 - Prob. 29E Ch. 16.5 - Prob. 30E Ch. 16.5 - Prob. 31E Ch. 16.5 - Prob. 32E Ch. 16.5 - Prob. 33E Ch. 16.5 - Prob. 34E Ch. 16.6 - Prob. 1PE Ch. 16.6 - Prob. 1E Ch. 16.6 - Prob. 2E Ch. 16.6 - Prob. 3E Ch. 16.6 - In Exercises 3–6, evaluate each determinant by...Ch. 16.6 - Prob. 5E Ch. 16.6 - In Exercises 3–6, evaluate each determinant by...Ch. 16.6 - Prob. 7E Ch. 16.6 - Prob. 8E Ch. 16.6 - Prob. 9E Ch. 16.6 - Prob. 10E Ch. 16.6 - Prob. 11E Ch. 16.6 - Prob. 12E Ch. 16.6 - Prob. 13E Ch. 16.6 - Prob. 14E Ch. 16.6 - Prob. 15E Ch. 16.6 - Prob. 16E Ch. 16.6 - Prob. 17E Ch. 16.6 - Prob. 18E Ch. 16.6 - Prob. 19E Ch. 16.6 - Prob. 20E Ch. 16.6 - Prob. 21E Ch. 16.6 - Prob. 22E Ch. 16.6 - Prob. 23E Ch. 16.6 - Prob. 24E Ch. 16.6 - Prob. 25E Ch. 16.6 - Prob. 26E Ch. 16.6 - Prob. 27E Ch. 16.6 - Prob. 28E Ch. 16.6 - Prob. 29E Ch. 16.6 - Prob. 30E Ch. 16.6 - Prob. 31E Ch. 16.6 - Prob. 32E Ch. 16.6 - Prob. 33E Ch. 16.6 - Prob. 34E Ch. 16.6 - Prob. 35E Ch. 16.6 - Prob. 36E Ch. 16.6 - Prob. 37E Ch. 16.6 - Prob. 38E Ch. 16 - Prob. 1RE Ch. 16 - Prob. 2RE Ch. 16 - Prob. 3RE Ch. 16 - Prob. 4RE Ch. 16 - Prob. 5RE Ch. 16 - Prob. 6RE Ch. 16 - Prob. 7RE Ch. 16 - Prob. 8RE Ch. 16 - Prob. 9RE Ch. 16 - Prob. 10RE Ch. 16 - Prob. 11RE Ch. 16 - Prob. 12RE Ch. 16 - Prob. 13RE Ch. 16 - Prob. 14RE Ch. 16 - Prob. 15RE Ch. 16 - Prob. 16RE Ch. 16 - Prob. 17RE Ch. 16 - Prob. 18RE Ch. 16 - Prob. 19RE Ch. 16 - Prob. 20RE Ch. 16 - Prob. 21RE Ch. 16 - Prob. 22RE Ch. 16 - Prob. 23RE Ch. 16 - Prob. 24RE Ch. 16 - Prob. 25RE Ch. 16 - Prob. 26RE Ch. 16 - Prob. 27RE Ch. 16 - Prob. 28RE Ch. 16 - Prob. 29RE Ch. 16 - Prob. 30RE Ch. 16 - Prob. 31RE Ch. 16 - Prob. 32RE Ch. 16 - Prob. 33RE Ch. 16 - Prob. 34RE Ch. 16 - Prob. 35RE Ch. 16 - Prob. 36RE Ch. 16 - Prob. 37RE Ch. 16 - Prob. 38RE Ch. 16 - Prob. 39RE Ch. 16 - Prob. 40RE Ch. 16 - Prob. 41RE Ch. 16 - Prob. 42RE Ch. 16 - Prob. 43RE Ch. 16 - Prob. 44RE Ch. 16 - Prob. 45RE Ch. 16 - Prob. 46RE Ch. 16 - Prob. 47RE Ch. 16 - Prob. 48RE Ch. 16 - Prob. 49RE Ch. 16 - Prob. 50RE Ch. 16 - Prob. 51RE Ch. 16 - Prob. 52RE Ch. 16 - Prob. 53RE Ch. 16 - Prob. 54RE Ch. 16 - Prob. 55RE Ch. 16 - Prob. 56RE Ch. 16 - Prob. 57RE Ch. 16 - Prob. 58RE Ch. 16 - Prob. 59RE Ch. 16 - Prob. 60RE Ch. 16 - Prob. 61RE Ch. 16 - Prob. 62RE Ch. 16 - Prob. 63RE Ch. 16 - Prob. 64RE Ch. 16 - Prob. 65RE Ch. 16 - Prob. 66RE Ch. 16 - Prob. 67RE Ch. 16 - In Exercises 67–70, use the determinants for...Ch. 16 - Prob. 69RE Ch. 16 - Prob. 70RE Ch. 16 - Prob. 71RE Ch. 16 - Prob. 72RE Ch. 16 - Prob. 73RE Ch. 16 - Prob. 74RE Ch. 16 - Prob. 75RE Ch. 16 - In Exercises 73–76, solve the given...Ch. 16 - Prob. 77RE Ch. 16 - Prob. 78RE Ch. 16 - Prob. 79RE Ch. 16 - Prob. 80RE Ch. 16 - Prob. 81RE Ch. 16 - Prob. 82RE Ch. 16 - Prob. 83RE Ch. 16 - Prob. 84RE Ch. 16 - Prob. 85RE Ch. 16 - Prob. 86RE Ch. 16 - Prob. 87RE Ch. 16 - Prob. 88RE Ch. 16 - Prob. 89RE Ch. 16 - Prob. 90RE Ch. 16 - Prob. 91RE Ch. 16 - Prob. 92RE Ch. 16 - Prob. 93RE Ch. 16 - Prob. 94RE Ch. 16 - Prob. 95RE Ch. 16 - Prob. 96RE Ch. 16 - Prob. 97RE Ch. 16 - Prob. 1PT Ch. 16 - Prob. 2PT Ch. 16 - Prob. 3PT Ch. 16 - Prob. 4PT Ch. 16 - Prob. 5PT Ch. 16 - Prob. 6PT Ch. 16 - Prob. 7PT Ch. 16 - Prob. 8PT Ch. 16 - Prob. 9PT Ch. 16 - Prob. 10PT

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.