 18.18.1: In Exercises 16, solve each equation or system of equations. 2x 3x ...
 18.18.2: In Exercises 16, solve each equation or system of equations. 2x2 5x 12
 18.18.3: In Exercises 16, solve each equation or system of equations. 8x 5y ...
 18.18.4: In Exercises 16, solve each equation or system of equations. 15 x 4...
 18.18.5: In Exercises 16, solve each equation or system of equations. 3x 7 8
 18.18.6: In Exercises 16, solve each equation or system of equations. If f (...
 18.18.7: In Exercises 711, simplify each expression 8x3 4x7
 18.18.8: In Exercises 711, simplify each expression 8 (3) 4
 18.18.9: In Exercises 711, simplify each expression 1 x 1 2 1 3 x 6
 18.18.10: In Exercises 711, simplify each expression 4 x2 3x2 5x 2
 18.18.11: In Exercises 711, simplify each expression 5 (8) (4 6)
 18.18.12: In Exercises 1213, factor completely. x2 18x 77
 18.18.13: In Exercises 1213, factor completely. x3 25x
 18.18.14: In Exercises 1417, perform the indicated operations. If possible, s...
 18.18.15: In Exercises 1417, perform the indicated operations. If possible, s...
 18.18.16: In Exercises 1417, perform the indicated operations. If possible, s...
 18.18.17: In Exercises 1417, perform the indicated operations. If possible, s...
 18.18.18: Solve the system: x 3y z 5 x 2y 3z 13 2x 5y z 8.
 18.18.19: In Exercises 1920, graph each equation in a rectangular coordinate ...
 18.18.20: In Exercises 1920, graph each equation in a rectangular coordinate ...
 18.18.21: Is {(1, 5), (2, 5), (3, 5), (4, 5), (6, 5)} a function? Give the re...
 18.18.22: Find the slope of the line through (1, 5) and (2, 3).
 18.18.23: Write the pointslope form of the equation of the line with slope 5...
 18.18.24: Multiply and write the answer in scientific notation: (7 108)(3 102).
 18.18.25: Find the domain of f(x) 1 15 x
Solutions for Chapter 18: CUMULATIVE REVIEW EXERCISES
Full solutions for Introductory & Intermediate Algebra for College Students  4th Edition
ISBN: 9780321758941
Solutions for Chapter 18: CUMULATIVE REVIEW EXERCISES
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Introductory & Intermediate Algebra for College Students, edition: 4. Introductory & Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758941. Since 25 problems in chapter 18: CUMULATIVE REVIEW EXERCISES have been answered, more than 75014 students have viewed full stepbystep solutions from this chapter. Chapter 18: CUMULATIVE REVIEW EXERCISES includes 25 full stepbystep solutions.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

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

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

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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

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

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.

Outer product uv T
= column times row = rank one matrix.

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

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

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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

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