 8.8.1: 12 involve credit cards that calculate interest using the average d...
 8.8.2: 12 involve credit cards that calculate interest using the average d...
 8.8.3: 34 involve credit cards that calculate interest using the average d...
 8.8.4: 34 involve credit cards that calculate interest using the average d...
 8.8.5: In 510, use PMT = Pa r n b c 1  a1 + r n b nt d to determine the ...
 8.8.6: In 510, use PMT = Pa r n b c 1  a1 + r n b nt d to determine the ...
 8.8.7: In 510, use PMT = Pa r n b c 1  a1 + r n b nt d to determine the ...
 8.8.8: In 510, use PMT = Pa r n b c 1  a1 + r n b nt d to determine the ...
 8.8.9: In 510, use PMT = Pa r n b c 1  a1 + r n b nt d to determine the ...
 8.8.10: In 510, use PMT = Pa r n b c 1  a1 + r n b nt d to determine the ...
 8.8.11: Describe the difference between a fixed installment loan and an ope...
 8.8.12: For a credit card billing period, describe how the average daily ba...
 8.8.13: Describe two advantages of using credit cards.
 8.8.14: Describe two disadvantages of using credit cards.
 8.8.15: What is a debit card?
 8.8.16: Describe what is contained in a credit report.
 8.8.17: What are credit scores?
 8.8.18: Describe two aspects of responsible credit card use.
 8.8.19: Make Sense? In 1925, determine whether each statement makes sense o...
 8.8.20: Make Sense? In 1925, determine whether each statement makes sense o...
 8.8.21: Make Sense? In 1925, determine whether each statement makes sense o...
 8.8.22: Make Sense? In 1925, determine whether each statement makes sense o...
 8.8.23: Make Sense? In 1925, determine whether each statement makes sense o...
 8.8.24: Make Sense? In 1925, determine whether each statement makes sense o...
 8.8.25: Make Sense? In 1925, determine whether each statement makes sense o...
 8.8.26: A bank bills its credit card holders on the first of each month for...
 8.8.27: Cellphone Plans If credit cards can cause financial woes, cellphone...
 8.8.28: Risky Credit Arrangements Group members should present a report on ...
Solutions for Chapter 8.8: Credit Cards
Full solutions for Thinking Mathematically  6th Edition
ISBN: 9780321867322
Solutions for Chapter 8.8: Credit Cards
Get Full SolutionsSince 28 problems in chapter 8.8: Credit Cards have been answered, more than 70849 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Thinking Mathematically, edition: 6. Chapter 8.8: Credit Cards includes 28 full stepbystep solutions. Thinking Mathematically was written by and is associated to the ISBN: 9780321867322. This expansive textbook survival guide covers the following chapters and their solutions.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

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.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

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

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

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.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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).

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 equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.