 10.1.1: APPLICATION There are four basic blood types. The distribution of t...
 10.1.2: Use the relative frequency circle graph in Exercise 1 to answer the...
 10.1.3: Which data set matches the relative frequency circle graph at right...
 10.1.4: In the relative frequency bar graph of the librarys collection crea...
 10.1.5: A manufacturer states that it produces colored candies according to...
 10.1.6: Chloe bought a small package of the candies described in Exercise 5...
 10.1.7: This table shows the number of students in each grade at a high sch...
 10.1.8: Match each bar graph with its corresponding circle graph. Try to do...
 10.1.9: What is a reasonable estimate of the chance that a randomly thrown ...
 10.1.10: Write an equation in general form for the parabola shown, with xin...
 10.1.11: Astrid works as an intern in a windmill park in Holland. She has le...
 10.1.12: APPLICATION In 2001 there were 3141 counties in the United States. ...
Solutions for Chapter 10.1: Relative Frequency Graphs
Full solutions for Discovering Algebra: An Investigative Approach  2nd Edition
ISBN: 9781559537636
Solutions for Chapter 10.1: Relative Frequency Graphs
Get Full SolutionsThis textbook survival guide was created for the textbook: Discovering Algebra: An Investigative Approach, edition: 2. This expansive textbook survival guide covers the following chapters and their solutions. Discovering Algebra: An Investigative Approach was written by Patricia and is associated to the ISBN: 9781559537636. Since 12 problems in chapter 10.1: Relative Frequency Graphs have been answered, more than 2877 students have viewed full stepbystep solutions from this chapter. Chapter 10.1: Relative Frequency Graphs includes 12 full stepbystep solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

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

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

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.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

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

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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

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

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

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

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.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.
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