 14.14.1.434: In Exercises 14, write the first four terms of each sequence whose ...
 14.14.1.435: In Exercises 14, write the first four terms of each sequence whose ...
 14.14.1.436: In Exercises 14, write the first four terms of each sequence whose ...
 14.14.1.437: In Exercises 14, write the first four terms of each sequence whose ...
 14.14.1.438: In Exercises 56, find each indicated sum. 5 i 1 (2i2 3)
 14.14.1.439: In Exercises 56, find each indicated sum. 4 i 0 (1)i 1i!
 14.14.1.440: In Exercises 78, express each sum using summation notation. Use i f...
 14.14.1.441: In Exercises 78, express each sum using summation notation. Use i f...
 14.14.1.442: In Exercises 911, write the first six terms of each arithmetic sequ...
 14.14.1.443: In Exercises 911, write the first six terms of each arithmetic sequ...
 14.14.1.444: In Exercises 911, write the first six terms of each arithmetic sequ...
 14.14.1.445: In Exercises 1214, use the formula for the general term (the nth te...
 14.14.1.446: In Exercises 1214, use the formula for the general term (the nth te...
 14.14.1.447: In Exercises 1214, use the formula for the general term (the nth te...
 14.14.1.448: In Exercises 1518, write a formula for the general term (the nth te...
 14.14.1.449: In Exercises 1518, write a formula for the general term (the nth te...
 14.14.1.450: In Exercises 1518, write a formula for the general term (the nth te...
 14.14.1.451: In Exercises 1518, write a formula for the general term (the nth te...
 14.14.1.452: Find the sum of the first 22 terms of the arithmetic sequence: 5, 1...
 14.14.1.453: Find the sum of the first 15 terms of the arithmetic sequence: 6, 3...
 14.14.1.454: Find 3 6 9 g 300, the sum of the first 100 positive multiples of 3.
 14.14.1.455: In Exercises 2224, use the formula for the sum of the first n terms...
 14.14.1.456: In Exercises 2224, use the formula for the sum of the first n terms...
 14.14.1.457: In Exercises 2224, use the formula for the sum of the first n terms...
 14.14.1.458: The graphic indicates that there are more eyes at school. 2005 In 2...
 14.14.1.459: A company offers a starting salary of $31,500 with raises of $2300 ...
 14.14.1.460: A theater has 25 seats in the first row and 35 rows in all. Each su...
 14.14.1.461: In Exercises 2831, write the first five terms of each geometric seq...
 14.14.1.462: In Exercises 2831, write the first five terms of each geometric seq...
 14.14.1.463: In Exercises 2831, write the first five terms of each geometric seq...
 14.14.1.464: In Exercises 2831, write the first five terms of each geometric seq...
 14.14.1.465: In Exercises 3234, use the formula for the general term (the nth te...
 14.14.1.466: In Exercises 3234, use the formula for the general term (the nth te...
 14.14.1.467: In Exercises 3234, use the formula for the general term (the nth te...
 14.14.1.468: In Exercises 3537, write a formula for the general term (the nth te...
 14.14.1.469: In Exercises 3537, write a formula for the general term (the nth te...
 14.14.1.470: In Exercises 3537, write a formula for the general term (the nth te...
 14.14.1.471: Find the sum of the first 15 terms of the geometric sequence: 5, 15...
 14.14.1.472: Find the sum of the first 7 terms of the geometric sequence: 8, 4, ...
 14.14.1.473: In Exercises 4042, use the formula for the sum of the first n terms...
 14.14.1.474: In Exercises 4042, use the formula for the sum of the first n terms...
 14.14.1.475: In Exercises 4042, use the formula for the sum of the first n terms...
 14.14.1.476: In Exercises 4346, find the sum of each infinite geometric series. ...
 14.14.1.477: In Exercises 4346, find the sum of each infinite geometric series. ...
 14.14.1.478: In Exercises 4346, find the sum of each infinite geometric series. ...
 14.14.1.479: In Exercises 4346, find the sum of each infinite geometric series. ...
 14.14.1.480: In Exercises 4748, express each repeating decimal as a fraction in ...
 14.14.1.481: In Exercises 4748, express each repeating decimal as a fraction in ...
 14.14.1.482: Projections for the U.S. population, ages 85 and older, are shown i...
 14.14.1.483: A job pays $32,000 for the first year with an annual increase of 6%...
 14.14.1.484: You spend $10 per week on lottery tickets, averaging $520 per year....
 14.14.1.485: To save for retirement, you decide to deposit $100 at the end of ea...
 14.14.1.486: A factory in an isolated town has an annual payroll of $4 million. ...
 14.14.1.487: In Exercises 5455, evaluate the given binomial coefficient. 11 8
 14.14.1.488: In Exercises 5455, evaluate the given binomial coefficient. 90 2
 14.14.1.489: In Exercises 5659, use the Binomial Theorem to expand each binomial...
 14.14.1.490: In Exercises 5659, use the Binomial Theorem to expand each binomial...
 14.14.1.491: In Exercises 5659, use the Binomial Theorem to expand each binomial...
 14.14.1.492: In Exercises 5659, use the Binomial Theorem to expand each binomial...
 14.14.1.493: In Exercises 6061, write the first three terms in each binomial exp...
 14.14.1.494: In Exercises 6061, write the first three terms in each binomial exp...
 14.14.1.495: In Exercises 6263, find the indicated term in each expansion. (x 2)...
 14.14.1.496: In Exercises 6263, find the indicated term in each expansion. (2x 3...
 14.14.1.497: Write the first five terms of the sequence whose general term is an...
 14.14.1.498: Find the indicated sum: 5 i 1 (i2 10).
 14.14.1.499: Express the sum using summation notation. Use i for the index of su...
 14.14.1.500: In Exercises 45, write a formula for the general term (the nth term...
 14.14.1.501: In Exercises 45, write a formula for the general term (the nth term...
 14.14.1.502: Find the sum of the first ten terms of the arithmetic sequence: 7, ...
 14.14.1.503: Find 20 i 1 (3i 4).
 14.14.1.504: In Exercises 89, use the formula for the sum of the first n terms o...
 14.14.1.505: In Exercises 89, use the formula for the sum of the first n terms o...
 14.14.1.506: Find the sum of the infinite geometric series: 4 4 2 4 22 4 23 g.
 14.14.1.507: Express 0.73 in fractional notation.
 14.14.1.508: A job pays $30,000 for the first year with an annual increase of 4%...
 14.14.1.509: Evaluate: 9 2.
 14.14.1.510: Use the Binomial. Theorem to expand and simplify: (x2 1)5.
 14.14.1.511: Use the Binomial Theorem to write the first three terms in the expa...
Solutions for Chapter 14: CHAPTER 14 REVIEW EXERCISES
Full solutions for Introductory & Intermediate Algebra for College Students  4th Edition
ISBN: 9780321758941
Solutions for Chapter 14: CHAPTER 14 REVIEW EXERCISES
Get Full SolutionsThis textbook survival guide was created for the textbook: Introductory & Intermediate Algebra for College Students, edition: 4. Since 78 problems in chapter 14: CHAPTER 14 REVIEW EXERCISES have been answered, more than 34399 students have viewed full stepbystep solutions from this chapter. Introductory & Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758941. Chapter 14: CHAPTER 14 REVIEW EXERCISES includes 78 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

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).

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.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

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

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.

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.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

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

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.