 151 .1: In a controlled experiment, two groups are formed to determine the ...
 151 .2: In the experiment described in Exercise 1, explain why it is necess...
 151 .3: In 35, organize the data in a stemandleaf diagram. The grades on ...
 151 .4: In 35, organize the data in a stemandleaf diagram. The weights of...
 151 .5: In 35, organize the data in a stemandleaf diagram. The heights, i...
 151 .6: In 68, organize the data in a frequency distribution table. The num...
 151 .7: In 68, organize the data in a frequency distribution table. The siz...
 151 .8: In 68, organize the data in a frequency distribution table. The num...
 151 .9: In 911, graph the histogram of each set of data. xi fi 3539 13 3034...
 151 .10: In 911, graph the histogram of each set of data. xi fi 101110 3 911...
 151 .11: In 911, graph the histogram of each set of data. xi fi $55$59 20 $5...
 151 .12: In 1218, suggest a method that might be used to collect data for ea...
 151 .13: In 1218, suggest a method that might be used to collect data for ea...
 151 .14: In 1218, suggest a method that might be used to collect data for ea...
 151 .15: In 1218, suggest a method that might be used to collect data for ea...
 151 .16: In 1218, suggest a method that might be used to collect data for ea...
 151 .17: In 1218, suggest a method that might be used to collect data for ea...
 151 .18: In 1218, suggest a method that might be used to collect data for ea...
 151 .19: The grades on a math test of 25 students are listed below. 86 92 77...
 151 .20: The stemandleaf diagram at the right shows the ages of 30 people ...
Solutions for Chapter 151 : GATHERING DATA
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 151 : GATHERING DATA
Get Full SolutionsAmsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. Chapter 151 : GATHERING DATA includes 20 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 20 problems in chapter 151 : GATHERING DATA have been answered, more than 28488 students have viewed full stepbystep solutions from this chapter.

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).

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

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

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

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

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

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

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

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

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

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.

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.