 11.5.11.1.227: A longterm loan in which the property is pledged as security for p...
 11.5.11.1.228: The amount of cash the buyer must pay to the seller before the lend...
 11.5.11.1.229: Interest prepaid by the buyer, which may be used to reduce the stat...
 11.5.11.1.230: The final step in the real estate sale process is called the .
 11.5.11.1.231: The buyers gross monthly income minus any fixed monthly payments wi...
 11.5.11.1.232: A list containing the payment number, payment on interest, payment ...
 11.5.11.1.233: In Exercises 710, determine the monthly principal and interest paym...
 11.5.11.1.234: In Exercises 710, determine the monthly principal and interest paym...
 11.5.11.1.235: In Exercises 710, determine the monthly principal and interest paym...
 11.5.11.1.236: In Exercises 710, determine the monthly principal and interest paym...
 11.5.11.1.237: Buying a House Anna Wasilewska is buying a house selling for $175,0...
 11.5.11.1.238: Buying a House Sadaf Din is purchasing a house selling for $215,000...
 11.5.11.1.239: Buying a Townhouse Karen Guardino is purchasing a brownstone townho...
 11.5.11.1.240: Buying a First House Rebecca Williams is purchasing her first house...
 11.5.11.1.241: Paying Points Martha Cutler is buying a house selling for $195,000....
 11.5.11.1.242: Down Payment and Points The Nicols are buying a house selling for $...
 11.5.11.1.243: Qualifying for a Mortgage Pietr and Helga Guenthers gross monthly i...
 11.5.11.1.244: Qualifying for a Mortgage TingFang and Suhua Zhengs gross monthly...
 11.5.11.1.245: A 30Year Conventional Mortgage Ingrid Holzner obtains a 30year, $...
 11.5.11.1.246: A 25Year Conventional Mortgage Mr. and Mrs. Alan Bell obtain a 25...
 11.5.11.1.247: Evaluating a Loan Request The Rosens found a house selling for $113...
 11.5.11.1.248: Evaluating a Loan Request Kathy Fields wants to buy a condominium s...
 11.5.11.1.249: Comparing Loans The Riveras are negotiating with two banks for a mo...
 11.5.11.1.250: Comparing Loans Paul Westerberg is negotiating with two credit unio...
 11.5.11.1.251: Changing Lengths of Mortgages Rose Hulman and her husband, George M...
 11.5.11.1.252: Comparing Payment Frequency Janet Samuels is purchasing a new house...
 11.5.11.1.253: An AdjustableRate Mortgage The Simpsons purchased a house for $105...
 11.5.11.1.254: An AdjustableRate Mortgage The Bretz family purchased a house for ...
 11.5.11.1.255: Comparing Mortgages The Hassads are applying for a $90,000 mortgage...
 11.5.11.1.256: Finding Your Dream Home Examine a local newspaper to find your drea...
 11.5.11.1.257: Closing Costs An important part of buying a house is the closing. T...
Solutions for Chapter 11.5: Consumer Mathematics
Full solutions for A Survey of Mathematics with Applications  9th Edition
ISBN: 9780321759665
Solutions for Chapter 11.5: Consumer Mathematics
Get Full SolutionsSince 31 problems in chapter 11.5: Consumer Mathematics have been answered, more than 79937 students have viewed full stepbystep solutions from this chapter. A Survey of Mathematics with Applications was written by and is associated to the ISBN: 9780321759665. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.5: Consumer Mathematics includes 31 full stepbystep solutions. This textbook survival guide was created for the textbook: A Survey of Mathematics with Applications, edition: 9.

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

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

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.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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).

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

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.