×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide

Solutions for Chapter 1.6: Inverse Functions

Precalculus With Limits A Graphing Approach | 5th Edition | ISBN: 9780618851522 | Authors: Ron Larson Robert Hostetler, Bruce H. Edwards, David C. Falvo (Contributor)

Full solutions for Precalculus With Limits A Graphing Approach | 5th Edition

ISBN: 9780618851522

Precalculus With Limits A Graphing Approach | 5th Edition | ISBN: 9780618851522 | Authors: Ron Larson Robert Hostetler, Bruce H. Edwards, David C. Falvo (Contributor)

Solutions for Chapter 1.6: Inverse Functions

Solutions for Chapter 1.6
4 5 0 363 Reviews
29
3
Textbook: Precalculus With Limits A Graphing Approach
Edition: 5
Author: Ron Larson Robert Hostetler, Bruce H. Edwards, David C. Falvo (Contributor)
ISBN: 9780618851522

Precalculus With Limits A Graphing Approach was written by and is associated to the ISBN: 9780618851522. Since 128 problems in chapter 1.6: Inverse Functions have been answered, more than 44106 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.6: Inverse Functions includes 128 full step-by-step solutions. This textbook survival guide was created for the textbook: Precalculus With Limits A Graphing Approach, edition: 5.

Key Math Terms and definitions covered in this textbook
  • Companion matrix.

    Put CI, ... ,Cn in row n and put n - 1 ones just above the main diagonal. Then det(A - AI) = ±(CI + c2A + C3A 2 + .•. + cnA n-l - An).

  • 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.

  • 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

  • Dimension of vector space

    dim(V) = number of vectors in any basis for V.

  • Free variable Xi.

    Column i has no pivot in elimination. We can give the n - r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

  • Gauss-Jordan method.

    Invert A by row operations on [A I] to reach [I A-I].

  • Hypercube matrix pl.

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

  • 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 .

  • Orthogonal subspaces.

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

  • Pivot.

    The diagonal entry (first nonzero) at the time when a row is used in elimination.

  • Positive definite matrix A.

    Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

  • Random matrix rand(n) or randn(n).

    MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

  • Right inverse A+.

    If A has full row rank m, then A+ = AT(AAT)-l has AA+ = 1m.

  • Semidefinite matrix A.

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

  • Solvable system Ax = b.

    The right side b is in the column space of A.

  • 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.

  • Tridiagonal matrix T: tij = 0 if Ii - j I > 1.

    T- 1 has rank 1 above and below diagonal.

  • Vector addition.

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

×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide
×
Reset your password