 9.4.9.4.1: Fill in the blanks. The procedure used to eliminate the xyterm in ...
 9.4.9.4.2: Fill in the blanks. Quantities that are equal in both the original ...
 9.4.9.4.3: Fill in the blanks. The quantity is called the _______ of the equat...
 9.4.9.4.4: In Exercises 314, rotate the axes to eliminate the xyterm in the e...
 9.4.9.4.5: In Exercises 314, rotate the axes to eliminate the xyterm in the e...
 9.4.9.4.6: In Exercises 314, rotate the axes to eliminate the xyterm in the e...
 9.4.9.4.7: In Exercises 314, rotate the axes to eliminate the xyterm in the e...
 9.4.9.4.8: In Exercises 314, rotate the axes to eliminate the xyterm in the e...
 9.4.9.4.9: In Exercises 314, rotate the axes to eliminate the xyterm in the e...
 9.4.9.4.10: In Exercises 314, rotate the axes to eliminate the xyterm in the e...
 9.4.9.4.11: In Exercises 314, rotate the axes to eliminate the xyterm in the e...
 9.4.9.4.12: In Exercises 314, rotate the axes to eliminate the xyterm in the e...
 9.4.9.4.13: In Exercises 314, rotate the axes to eliminate the xyterm in the e...
 9.4.9.4.14: In Exercises 314, rotate the axes to eliminate the xyterm in the e...
 9.4.9.4.15: In Exercises 1520, use a graphing utility to graph the conic. Deter...
 9.4.9.4.16: In Exercises 1520, use a graphing utility to graph the conic. Deter...
 9.4.9.4.17: In Exercises 1520, use a graphing utility to graph the conic. Deter...
 9.4.9.4.18: In Exercises 1520, use a graphing utility to graph the conic. Deter...
 9.4.9.4.19: In Exercises 1520, use a graphing utility to graph the conic. Deter...
 9.4.9.4.20: In Exercises 1520, use a graphing utility to graph the conic. Deter...
 9.4.9.4.21: In Exercises 2126, match the graph with its equation. [The graphs a...
 9.4.9.4.22: In Exercises 2126, match the graph with its equation. [The graphs a...
 9.4.9.4.23: In Exercises 2126, match the graph with its equation. [The graphs a...
 9.4.9.4.24: In Exercises 2126, match the graph with its equation. [The graphs a...
 9.4.9.4.25: In Exercises 2126, match the graph with its equation. [The graphs a...
 9.4.9.4.26: In Exercises 2126, match the graph with its equation. [The graphs a...
 9.4.9.4.27: In Exercises 2734, (a) use the discriminant to classify the graph o...
 9.4.9.4.28: In Exercises 2734, (a) use the discriminant to classify the graph o...
 9.4.9.4.29: In Exercises 2734, (a) use the discriminant to classify the graph o...
 9.4.9.4.30: In Exercises 2734, (a) use the discriminant to classify the graph o...
 9.4.9.4.31: In Exercises 2734, (a) use the discriminant to classify the graph o...
 9.4.9.4.32: In Exercises 2734, (a) use the discriminant to classify the graph o...
 9.4.9.4.33: In Exercises 2734, (a) use the discriminant to classify the graph o...
 9.4.9.4.34: In Exercises 2734, (a) use the discriminant to classify the graph o...
 9.4.9.4.35: In Exercises 3538, sketch (if possible) the graph of the degenerate...
 9.4.9.4.36: In Exercises 3538, sketch (if possible) the graph of the degenerate...
 9.4.9.4.37: In Exercises 3538, sketch (if possible) the graph of the degenerate...
 9.4.9.4.38: In Exercises 3538, sketch (if possible) the graph of the degenerate...
 9.4.9.4.39: In Exercises 3946, solve the system of quadratic equations algebrai...
 9.4.9.4.40: In Exercises 3946, solve the system of quadratic equations algebrai...
 9.4.9.4.41: In Exercises 3946, solve the system of quadratic equations algebrai...
 9.4.9.4.42: In Exercises 3946, solve the system of quadratic equations algebrai...
 9.4.9.4.43: In Exercises 3946, solve the system of quadratic equations algebrai...
 9.4.9.4.44: In Exercises 3946, solve the system of quadratic equations algebrai...
 9.4.9.4.45: In Exercises 3946, solve the system of quadratic equations algebrai...
 9.4.9.4.46: In Exercises 3946, solve the system of quadratic equations algebrai...
 9.4.9.4.47: In Exercises 4752, solve the system of quadratic equations algebrai...
 9.4.9.4.48: In Exercises 4752, solve the system of quadratic equations algebrai...
 9.4.9.4.49: In Exercises 4752, solve the system of quadratic equations algebrai...
 9.4.9.4.50: In Exercises 4752, solve the system of quadratic equations algebrai...
 9.4.9.4.51: In Exercises 4752, solve the system of quadratic equations algebrai...
 9.4.9.4.52: In Exercises 4752, solve the system of quadratic equations algebrai...
 9.4.9.4.53: True or False? In Exercises 53 and 54, determine whether the statem...
 9.4.9.4.54: True or False? In Exercises 53 and 54, determine whether the statem...
 9.4.9.4.55: In Exercises 5558, sketch the graph of the rational function. Ident...
 9.4.9.4.56: In Exercises 5558, sketch the graph of the rational function. Ident...
 9.4.9.4.57: In Exercises 5558, sketch the graph of the rational function. Ident...
 9.4.9.4.58: In Exercises 5558, sketch the graph of the rational function. Ident...
 9.4.9.4.59: In Exercises 5962, if possible, find (a) AB, (b) BA, and (c)
 9.4.9.4.60: In Exercises 5962, if possible, find (a) AB, (b) BA, and (c)
 9.4.9.4.61: In Exercises 5962, if possible, find (a) AB, (b) BA, and (c)
 9.4.9.4.62: In Exercises 5962, if possible, find (a) AB, (b) BA, and (c)
 9.4.9.4.63: In Exercises 6370, graph the function.
 9.4.9.4.64: In Exercises 6370, graph the function.
 9.4.9.4.65: In Exercises 6370, graph the function.
 9.4.9.4.66: In Exercises 6370, graph the function.
 9.4.9.4.67: In Exercises 6370, graph the function.
 9.4.9.4.68: In Exercises 6370, graph the function.
 9.4.9.4.69: In Exercises 6370, graph the function.
 9.4.9.4.70: In Exercises 6370, graph the function.
 9.4.9.4.71: In Exercises 7174, find the area of the triangle.
 9.4.9.4.72: In Exercises 7174, find the area of the triangle.
 9.4.9.4.73: In Exercises 7174, find the area of the triangle.
 9.4.9.4.74: In Exercises 7174, find the area of the triangle.
Solutions for Chapter 9.4: Rotation and Systems of Quadratic Equations
Full solutions for Precalculus With Limits A Graphing Approach  5th Edition
ISBN: 9780618851522
Solutions for Chapter 9.4: Rotation and Systems of Quadratic Equations
Get Full SolutionsChapter 9.4: Rotation and Systems of Quadratic Equations includes 74 full stepbystep solutions. This textbook survival guide was created for the textbook: Precalculus With Limits A Graphing Approach, edition: 5. Since 74 problems in chapter 9.4: Rotation and Systems of Quadratic Equations have been answered, more than 102525 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Precalculus With Limits A Graphing Approach was written by and is associated to the ISBN: 9780618851522.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

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

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

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

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

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

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

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

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.

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!

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

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

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