 164.1: There are 20 students in a club, 12 boys and 8 girls. If five membe...
 164.2: Hunter said that the number of combinations of n things taken r at ...
 164.3: In 36, find exact probabilities showing all required computation.A ...
 164.4: In 36, find exact probabilities showing all required computation.A ...
 164.5: In 36, find exact probabilities showing all required computation.A ...
 164.6: In 36, find exact probabilities showing all required computation.A ...
 164.7: In 714, answers can be rounded to four decimal places.The probabili...
 164.8: In 714, answers can be rounded to four decimal places.Jacks batting...
 164.9: In 714, answers can be rounded to four decimal places.Marie plays s...
 164.10: In 714, answers can be rounded to four decimal places.A fastfood r...
 164.11: In 714, answers can be rounded to four decimal places.A store estim...
 164.12: In 714, answers can be rounded to four decimal places.Assume that t...
 164.13: In 714, answers can be rounded to four decimal places.Using a speci...
 164.14: In 714, answers can be rounded to four decimal places.Statisticians...
Solutions for Chapter 164: PROBABILITY WITH TWO OUTCOMES
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 164: PROBABILITY WITH TWO OUTCOMES
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 14 problems in chapter 164: PROBABILITY WITH TWO OUTCOMES have been answered, more than 29295 students have viewed full stepbystep solutions from this chapter. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. Chapter 164: PROBABILITY WITH TWO OUTCOMES includes 14 full stepbystep solutions. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1.

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

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).

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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

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

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

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.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

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

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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

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.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Solvable system Ax = b.
The right side b is in the column space of A.

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

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

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