 11.6.1: If are the rectangular coordinates of a point P and are its polar c...
 11.6.2: Transform the equation from polar coordinates to rectangular coordi...
 11.6.3: A is the set of points P in the plane such that the ratio of the di...
 11.6.4: The eccentricity e of a parabola is , of an ellipse it is , and of ...
 11.6.5: True or False If are polar coordinates, the equation r = 22 + 3 sin...
 11.6.6: True or False The eccentricity e of any conic is where a is the dis...
 11.6.7: In 712, identify the conic that each polar equation represents.Also...
 11.6.8: In 712, identify the conic that each polar equation represents.Also...
 11.6.9: In 712, identify the conic that each polar equation represents.Also...
 11.6.10: In 712, identify the conic that each polar equation represents.Also...
 11.6.11: In 712, identify the conic that each polar equation represents.Also...
 11.6.12: In 712, identify the conic that each polar equation represents.Also...
 11.6.13: In 1324, analyze each equation and graph it.
 11.6.14: In 1324, analyze each equation and graph it.
 11.6.15: In 1324, analyze each equation and graph it.
 11.6.16: In 1324, analyze each equation and graph it.
 11.6.17: In 1324, analyze each equation and graph it.
 11.6.18: In 1324, analyze each equation and graph it.
 11.6.19: In 1324, analyze each equation and graph it.
 11.6.20: In 1324, analyze each equation and graph it.
 11.6.21: In 1324, analyze each equation and graph it.
 11.6.22: In 1324, analyze each equation and graph it.
 11.6.23: In 1324, analyze each equation and graph it.
 11.6.24: In 1324, analyze each equation and graph it.
 11.6.25: In 2536, convert each polar equation to a rectangular equation.
 11.6.26: In 2536, convert each polar equation to a rectangular equation.
 11.6.27: In 2536, convert each polar equation to a rectangular equation.
 11.6.28: In 2536, convert each polar equation to a rectangular equation.
 11.6.29: In 2536, convert each polar equation to a rectangular equation.
 11.6.30: In 2536, convert each polar equation to a rectangular equation.
 11.6.31: In 2536, convert each polar equation to a rectangular equation.
 11.6.32: In 2536, convert each polar equation to a rectangular equation.
 11.6.33: In 2536, convert each polar equation to a rectangular equation.
 11.6.34: In 2536, convert each polar equation to a rectangular equation.
 11.6.35: In 2536, convert each polar equation to a rectangular equation.
 11.6.36: In 2536, convert each polar equation to a rectangular equation.
 11.6.37: In 3742, find a polar equation for each conic. For each, a focus is...
 11.6.38: In 3742, find a polar equation for each conic. For each, a focus is...
 11.6.39: In 3742, find a polar equation for each conic. For each, a focus is...
 11.6.40: In 3742, find a polar equation for each conic. For each, a focus is...
 11.6.41: In 3742, find a polar equation for each conic. For each, a focus is...
 11.6.42: In 3742, find a polar equation for each conic. For each, a focus is...
 11.6.43: Derive equation (b) in Table 5:r = ep 1 + e cos u
 11.6.44: Derive equation (c) in Table 5:r = ep 1 + e sin u
 11.6.45: Derive equation (d) in Table 5:r = ep 1  e sin u
 11.6.46: Orbit of Mercury The planet Mercury travels around the Sun in an el...
Solutions for Chapter 11.6: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 11.6
Get Full SolutionsThis textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. Since 46 problems in chapter 11.6 have been answered, more than 58434 students have viewed full stepbystep solutions from this chapter. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.6 includes 46 full stepbystep solutions.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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

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.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

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

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 •

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

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.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

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

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

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

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

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

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).