 103.1: Carolyn Luttrell owns Just the Right Thing, a small antiques shop w...
 103.2: Hughes Trailer Manufacturer makes utility trailers and has seven em...
 103.3: Determine the employers deposit of withholding, Social Security, an...
 103.4: Heaven Sent Gifts, a small business that provides custom meals, flo...
 103.5: How much SUTA tax must Bruces employer pay for him?
 103.6: How much FUTA tax must Bruces company pay for him?
 103.7: Bailey Plyler has three employees in his carpet cleaning business. ...
Solutions for Chapter 103: THE EMPLOYERS PAYROLL TAXES
Full solutions for Business Math,  9th Edition
ISBN: 9780135108178
Solutions for Chapter 103: THE EMPLOYERS PAYROLL TAXES
Get Full SolutionsThis textbook survival guide was created for the textbook: Business Math, , edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 103: THE EMPLOYERS PAYROLL TAXES includes 7 full stepbystep solutions. Business Math, was written by and is associated to the ISBN: 9780135108178. Since 7 problems in chapter 103: THE EMPLOYERS PAYROLL TAXES have been answered, more than 17927 students have viewed full stepbystep solutions from this chapter.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

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

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

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

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

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

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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

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.

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

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

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