- 11-3.1: Jos makes a simple discount note with a face value of $2,500, a ter...
- 11-3.2: Find the proceeds for Exercise 1.
- 11-3.3: Find the discount and proceeds on a $3,250 face-value note for six ...
- 11-3.4: Find the maturity value of the undiscounted promissory note shown i...
- 11-3.5: Roland Clark has a simple discount note for $6,500, at an ordinary ...
- 11-3.6: What is the effective interest rate of a simple discount note for $...
- 11-3.7: Shanquayle Jenkins needs to calculate the effective interest rate o...
- 11-3.8: Matt Crouse needs to calculate the effective interest rate of a sim...
- 11-3.9: Carter Manufacturing holds a note of $5,000 that has an interest ra...
- 11-3.10: Discuss reasons a payee might agree to a non-interestbearing note.
- 11-3.11: Discuss reasons a payee would sell a note to a third party and lose...
Solutions for Chapter 11-3: PROMISSORY NOTES
Full solutions for Business Math, | 9th Edition
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
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 A-I.
Square matrix with A-I A = I and AA-l = 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 B-1 A-I and (A-I)T. Cofactor formula (A-l)ij = Cji! detA.
lA-II = 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+ (Moore-Penrose 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.
Skew-symmetric 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).
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. A-I is also symmetric.
Constant down each diagonal = time-invariant (shift-invariant) filter.