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Solutions for Chapter 1.3: Five-Number Summaries and Box Plots

Discovering Algebra: An Investigative Approach | 2nd Edition | ISBN: 9781559537636 | Authors: Jerald Murdock, Ellen Kamischke, Eric Kamischke

Full solutions for Discovering Algebra: An Investigative Approach | 2nd Edition

ISBN: 9781559537636

Discovering Algebra: An Investigative Approach | 2nd Edition | ISBN: 9781559537636 | Authors: Jerald Murdock, Ellen Kamischke, Eric Kamischke

Solutions for Chapter 1.3: Five-Number Summaries and Box Plots

Chapter 1.3: Five-Number Summaries and Box Plots includes 12 full step-by-step solutions. Since 12 problems in chapter 1.3: Five-Number Summaries and Box Plots have been answered, more than 7690 students have viewed full step-by-step solutions from this chapter. Discovering Algebra: An Investigative Approach was written by and is associated to the ISBN: 9781559537636. This textbook survival guide was created for the textbook: Discovering Algebra: An Investigative Approach, edition: 2. This expansive textbook survival guide covers the following chapters and their solutions.

Key Math Terms and definitions covered in this textbook
  • Cayley-Hamilton Theorem.

    peA) = det(A - AI) has peA) = zero matrix.

  • 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.

  • Eigenvalue A and eigenvector x.

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

  • Fast Fourier Transform (FFT).

    A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn-1c can be computed with ne/2 multiplications. Revolutionary.

  • Fibonacci numbers

    0,1,1,2,3,5, ... satisfy Fn = Fn-l + Fn- 2 = (A7 -A~)I()q -A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

  • Free columns of A.

    Columns without pivots; these are combinations of earlier columns.

  • Least squares solution X.

    The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b - Ax is orthogonal to all columns of A.

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

    Vector addition and scalar multiplication.

  • Nullspace N (A)

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

  • 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).

  • Projection matrix P onto subspace S.

    Projection p = P b is the closest point to b in S, error e = b - Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) -1 AT.

  • Schur complement S, D - C A -} B.

    Appears in block elimination on [~ g ].

  • Semidefinite matrix A.

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

  • Spanning set.

    Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

  • Standard basis for Rn.

    Columns of n by n identity matrix (written i ,j ,k in R3).

  • 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.

  • Trace of A

    = sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

  • Vector space V.

    Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

  • Vector v in Rn.

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

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