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Solutions for Chapter 18-1: INVENTORY

Full solutions for Business Math, | 9th Edition

ISBN: 9780135108178

Solutions for Chapter 18-1: INVENTORY

Solutions for Chapter 18-1
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ISBN: 9780135108178

Business Math, was written by and is associated to the ISBN: 9780135108178. This expansive textbook survival guide covers the following chapters and their solutions. Since 28 problems in chapter 18-1: INVENTORY have been answered, more than 19480 students have viewed full step-by-step solutions from this chapter. Chapter 18-1: INVENTORY includes 28 full step-by-step solutions. This textbook survival guide was created for the textbook: Business Math, , edition: 9.

Key Math Terms and definitions covered in this textbook
• 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.

• Cholesky factorization

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

• Column space C (A) =

space of all combinations of the columns of A.

• Complex conjugate

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

• Cramer's Rule for Ax = b.

B j has b replacing column j of A; x j = det B j I det A

• Eigenvalue A and eigenvector x.

Ax = AX with x#-O so det(A - AI) = o.

• Hypercube matrix pl.

Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

• Independent vectors VI, .. " vk.

No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

• Iterative method.

A sequence of steps intended to approach the desired solution.

• Linear combination cv + d w or L C jV j.

Vector addition and scalar multiplication.

• Matrix multiplication AB.

The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

• Minimal polynomial of A.

The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A - AI) if no eigenvalues are repeated; always meA) divides peA).

• 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.

• Normal matrix.

If N NT = NT N, then N has orthonormal (complex) eigenvectors.

• 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).

• Pivot columns of A.

Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

• 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).

• Rank r (A)

= number of pivots = dimension of column space = dimension of row space.

• Semidefinite matrix A.

(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

• Symmetric factorizations A = LDLT and A = QAQT.

Signs in A = signs in D.

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