 4.5.1: Write the pointslope form of the equation for each line graphed be...
 4.5.2: Look at each graph in Exercise 1 and estimate the yintercept. Then...
 4.5.3: Graph each linear equation on your calculator and name the xinterc...
 4.5.4: APPLICATION Carbon dioxide is one of several greenhouse gases that ...
 4.5.5: APPLICATION Alex collected this table of data by using two thermome...
 4.5.6: APPLICATION The table lists the concentration of dissolved oxygen (...
 4.5.7: Use the data and the equation you found in Exercise 6. a. Write an ...
 4.5.8: MiniInvestigation Scoop has a rolling ice cream cart. He recorded ...
 4.5.9: APPLICATION Bryan has bought a box of biscuits for his dog, Anchor....
 4.5.10: Solve the equation 2x 3(y + 1) = 12 for y by copying and filling in...
 4.5.11: Youve worked with various types of problems involving rates. A new ...
Solutions for Chapter 4.5: Writing PointSlope Equations to Fit Data
Full solutions for Discovering Algebra: An Investigative Approach  2nd Edition
ISBN: 9781559537636
Solutions for Chapter 4.5: Writing PointSlope Equations to Fit Data
Get Full SolutionsSince 11 problems in chapter 4.5: Writing PointSlope Equations to Fit Data have been answered, more than 2880 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 4.5: Writing PointSlope Equations to Fit Data includes 11 full stepbystep solutions. This textbook survival guide was created for the textbook: Discovering Algebra: An Investigative Approach, edition: 2. Discovering Algebra: An Investigative Approach was written by Patricia and is associated to the ISBN: 9781559537636.

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.)

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

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.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

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.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

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).

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

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.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

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

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