 1.7.1: In Exercises 15, determine the equations of the polynomials of deg...
 1.7.2: In Exercises 15, determine the equations of the polynomials of deg...
 1.7.3: In Exercises 15, determine the equations of the polynomials of deg...
 1.7.4: In Exercises 15, determine the equations of the polynomials of deg...
 1.7.5: In Exercises 15, determine the equations of the polynomials of deg...
 1.7.6: Find the equation of the polynomial of degree three whose graph pas...
 1.7.7: In Exercises 714, determine the currents in the various branches o...
 1.7.8: In Exercises 714, determine the currents in the various branches o...
 1.7.9: In Exercises 714, determine the currents in the various branches o...
 1.7.10: In Exercises 714, determine the currents in the various branches o...
 1.7.11: In Exercises 714, determine the currents in the various branches o...
 1.7.12: In Exercises 714, determine the currents in the various branches o...
 1.7.13: In Exercises 714, determine the currents in the various branches o...
 1.7.14: In Exercises 714, determine the currents in the various branches o...
 1.7.15: Determine the currents through the various branches of the electric...
 1.7.16: Construct a system of linear equations that describes the traffic f...
 1.7.17: Figure 1.32 represents the traffic entering and leaving a "roundabo...
 1.7.18: Figure 1.33 represents the traffic entering and leaving another typ...
 1.7.19: Figure 1.34 describes a flow of traffic, the units being vehicles p...
 1.7.20: There will be many polynomials of degree 2 that pass through the po...
 1.7.21: There will be many polynomials of degree 3 that pass through the po...
Solutions for Chapter 1.7: Curve Fitting, Electrical Networks, and Traffic Flow
Full solutions for Linear Algebra with Applications  8th Edition
ISBN: 9781449679545
Solutions for Chapter 1.7: Curve Fitting, Electrical Networks, and Traffic Flow
Get Full SolutionsSince 21 problems in chapter 1.7: Curve Fitting, Electrical Networks, and Traffic Flow have been answered, more than 8117 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Linear Algebra with Applications, edition: 8. Chapter 1.7: Curve Fitting, Electrical Networks, and Traffic Flow includes 21 full stepbystep solutions. Linear Algebra with Applications was written by and is associated to the ISBN: 9781449679545.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Iterative method.
A sequence of steps intended to approach the desired solution.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.