Introduction to Linear Algebra 5th. Edition by Lee W. Johnson, R. Dean Riess, Jimmy T. Arnold | 9780201658590 | 201658593 | Holooly

Introduction to Linear Algebra [EXP-51237]

299 SOLVED PROBLEMS

Question: 1.1.2

(a) Display the system of equations with coefficients a11 = 2, a12 = −1, a13 = −3, a21 = −2, a22 = 2, and a23 = 5, and with constants b1 = −1 and b2 = 3. (b) Verify that x1 = 1, x2 = 0, x3 = 1 is a solution for the system.

Verified Answer:

(a) The system is

2 x_{1}-x_{2}-3 x_{3}=-1[...

Question: 2.1.4

(a) Let v = →AB where A = (1, 5) and B = (3, 2). Represent v as an algebraic vector. (b) Let u = [4 7]. Represent u as a geometric vector with initial point C = (5. -2).

Verified Answer:

(a) Using part (a) of Table 2.1,

v =\left[\...

Question: 1.4.1

(a) Set up a system of equations that represents traffic flow for the network shown in Fig. 1.11. (The numbers give the average flows into and out of the network at peak traffic hours.) (b) Solve the system of equations. What is the traffic flow if x6 = 300 and x7 = 1300 vehicles per hour?

Verified Answer:

(a) Since the flow into a node is equal to the flo...

Question: 2.1.3

A geometric vector v has x-component 3 and y-component -5. (a) If we want to represent v in the form v = →AB where A = (1, 2) , what are the coordinates of the terminal point B? (b) If we want to represent v in the form v = →CD where D = (5, 7), what are the coordinates of the initial point C?

Verified Answer:

(a) By (2), the coordinates of Bare (1 + 3, 2 + (-...

Question: 4.8.5

An automobile rental company has three locations, which we designate as P, Q, and R. When an automobile is rented at one of the locations, it may be returned to any of the three locations. Suppose, at some specific time, that there are p cars at location P, q cars at Q, and r cars at R.

Verified Answer:

Let

x _{k}

represent the state of t...

Question: 3.9.4

As a final example to illustrate how MATLAB treats inconsistent square systems, find a least-squares solution to Ax = b where A = [2 3 5 1 0 3 3 3 8], b = [1 1 1].

Verified Answer:

The results are given in Fig.3.33 where, for clari...

Question: 4.2.8

Calculate det(A), det(B), and det(AB) for the matrices A = [1 2 -1 1] and B = [2 3 1 -1].

Verified Answer:

The product, AB, is given by

A B=\left[\beg...

Question: 7.7.2

Calculate the matrix p(A), where A = [1 −2 2 3] and where p(t) is the characteristic polynomial for A.

Verified Answer:

The characteristic polynomial for A is given by [l...

Question: 7.1.3

Classify the quadratic form q(r, s) = 3r^2 − 4rs + 3s^2.

Verified Answer:

We first find the matrix representation for q(x) =...

Question: 6.2.4

Compute det(A), where A = [1 2 0 2 −1 2 3 1 −3 2 −1 0 2 −3 −2 1].

Verified Answer:

The matrix A is (4 × 4). Using n = 4 in Definition...

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