 62.1: Virginia said that Example 3 could have been solved without using e...
 62.2: Pedro said that to form a sequence of five terms that begins with 2...
 62.3: In 38, determine if each sequence is an arithmetic sequence. If the...
 62.4: In 38, determine if each sequence is an arithmetic sequence. If the...
 62.5: In 38, determine if each sequence is an arithmetic sequence. If the...
 62.6: In 38, determine if each sequence is an arithmetic sequence. If the...
 62.7: In 38, determine if each sequence is an arithmetic sequence. If the...
 62.8: In 38, determine if each sequence is an arithmetic sequence. If the...
 62.9: In 914: a. Find the common difference of each arithmetic sequence. ...
 62.10: In 914: a. Find the common difference of each arithmetic sequence. ...
 62.11: In 914: a. Find the common difference of each arithmetic sequence. ...
 62.12: In 914: a. Find the common difference of each arithmetic sequence. ...
 62.13: In 914: a. Find the common difference of each arithmetic sequence. ...
 62.14: In 914: a. Find the common difference of each arithmetic sequence. ...
 62.15: Write the first six terms of the arithmetic sequence that has 12 fo...
 62.16: Write the first nine terms of the arithmetic sequence that has 100 ...
 62.17: Find four arithmetic means between 3 and 18.
 62.18: Find two arithmetic means between 1 and 5.
 62.19: Write a recursive definition for an arithmetic sequence with a comm...
 62.20: On July 1, Mr. Taylor owed $6,000. On the 1st of each of the follow...
 62.21: Li is developing a fitness program that includes doing pushups eac...
 62.22: a. Show that a linear function whose domain is the set of positive ...
 62.23: Leslie noticed that the daily number of email messages she receive...
Solutions for Chapter 62: Arithmetic Sequences
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 62: Arithmetic Sequences
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 62: Arithmetic Sequences includes 23 full stepbystep solutions. Since 23 problems in chapter 62: Arithmetic Sequences have been answered, more than 28612 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

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

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

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 .

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

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

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.