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# Solutions for Chapter 6.2: Compound Interest

## Full solutions for Finite Mathematics, Binder Ready Version: An Applied Approach | 11th Edition

ISBN: 9780470876398

Solutions for Chapter 6.2: Compound Interest

Solutions for Chapter 6.2
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##### ISBN: 9780470876398

This expansive textbook survival guide covers the following chapters and their solutions. Since 97 problems in chapter 6.2: Compound Interest have been answered, more than 16831 students have viewed full step-by-step solutions from this chapter. Finite Mathematics, Binder Ready Version: An Applied Approach was written by and is associated to the ISBN: 9780470876398. This textbook survival guide was created for the textbook: Finite Mathematics, Binder Ready Version: An Applied Approach, edition: 11. Chapter 6.2: Compound Interest includes 97 full step-by-step solutions.

Key Math Terms and definitions covered in this textbook
• Characteristic equation det(A - AI) = O.

The n roots are the eigenvalues of A.

• Cofactor Cij.

Remove row i and column j; multiply the determinant by (-I)i + j •

• Complete solution x = x p + Xn to Ax = b.

(Particular x p) + (x n in nullspace).

• 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. Block-diagonal: zero outside square blocks Du.

• Distributive Law

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

• Factorization

A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to 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.

• Indefinite matrix.

A symmetric matrix with eigenvalues of both signs (+ and - ).

• Iterative method.

A sequence of steps intended to approach the desired solution.

• Kronecker product (tensor product) A ® B.

Blocks aij B, eigenvalues Ap(A)Aq(B).

• Krylov subspace Kj(A, b).

The subspace spanned by b, Ab, ... , Aj-Ib. 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.

• Left nullspace N (AT).

Nullspace of AT = "left nullspace" of A because y T A = OT.

• Multiplier eij.

The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

• 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.

• Nullspace N (A)

= All solutions to Ax = O. Dimension n - r = (# columns) - rank.

• Rank r (A)

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

• Toeplitz matrix.

Constant down each diagonal = time-invariant (shift-invariant) filter.

v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

• Volume of box.

The rows (or the columns) of A generate a box with volume I det(A) I.

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