 2.5.1: Rewrite each equation in Y = form. a. xy = 15 b. xy = 35 c. xy = 3
 2.5.2: Two quantities, x and y, are inversely proportional. When x = 3, y ...
 2.5.3: Find five points that satisfy the inverse variation equation Graph ...
 2.5.4: Henry noticed that the more television he atched, the less time he ...
 2.5.5: APPLICATION The amount of time it takes to travel a given distance ...
 2.5.6: For each table of x and yvalues below, decide if the values show ...
 2.5.7: APPLICATION In Example A, you learned that the force in newtons nee...
 2.5.8: APPLICATION Emily and her little brother Sid are playing on a seesa...
 2.5.9: To use a doublepan balance, you put the object to be weighed on on...
 2.5.10: APPLICATION The student council wants to raise $10,000 to purchase ...
 2.5.11: A tuning fork vibrates at a particular frequency to make the sound ...
 2.5.12: APPLICATION To squeeze a given amount of air into a smaller and sma...
 2.5.13: APPLICATION A CD is on sale for 15% off its normal price of $13.95....
 2.5.14: Calcium and phosphorus play important roles in building human bones...
 2.5.15: APPLICATION Two dozen units in an apartment complex need to be pain...
 2.5.16: Sulfuric acid, a highly corrosive substance, is used in the manufac...
Solutions for Chapter 2.5: Inverse Variation
Full solutions for Discovering Algebra: An Investigative Approach  2nd Edition
ISBN: 9781559537636
Solutions for Chapter 2.5: Inverse Variation
Get Full SolutionsThis textbook survival guide was created for the textbook: Discovering Algebra: An Investigative Approach, edition: 2. Since 16 problems in chapter 2.5: Inverse Variation have been answered, more than 9782 students have viewed full stepbystep solutions from this chapter. Discovering Algebra: An Investigative Approach was written by and is associated to the ISBN: 9781559537636. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.5: Inverse Variation includes 16 full stepbystep solutions.

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.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

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 columns of A.
Columns without pivots; these are combinations of earlier columns.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

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

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

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

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

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

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.

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).

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

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

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.

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

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

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