 113.1: Jos makes a simple discount note with a face value of $2,500, a ter...
 113.2: Find the proceeds for Exercise 1.
 113.3: Find the discount and proceeds on a $3,250 facevalue note for six ...
 113.4: Find the maturity value of the undiscounted promissory note shown i...
 113.5: Roland Clark has a simple discount note for $6,500, at an ordinary ...
 113.6: What is the effective interest rate of a simple discount note for $...
 113.7: Shanquayle Jenkins needs to calculate the effective interest rate o...
 113.8: Matt Crouse needs to calculate the effective interest rate of a sim...
 113.9: Carter Manufacturing holds a note of $5,000 that has an interest ra...
 113.10: Discuss reasons a payee might agree to a noninterestbearing note.
 113.11: Discuss reasons a payee would sell a note to a third party and lose...
Solutions for Chapter 113: PROMISSORY NOTES
Full solutions for Business Math,  9th Edition
ISBN: 9780135108178
Solutions for Chapter 113: PROMISSORY NOTES
Get Full SolutionsChapter 113: PROMISSORY NOTES includes 11 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 11 problems in chapter 113: PROMISSORY NOTES have been answered, more than 18282 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Business Math, , edition: 9. Business Math, was written by and is associated to the ISBN: 9780135108178.

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

Column space C (A) =
space of all combinations of the columns of A.

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

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

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

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

Outer product uv T
= column times row = rank one matrix.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

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).

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.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Solvable system Ax = b.
The right side b is in the column space of A.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

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

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

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