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Textbooks > Math > Intermediate Algebra for College Students 6

Intermediate Algebra for College Students 6th Edition - Solutions by Chapter

Full solutions for Intermediate Algebra for College Students | 6th Edition

ISBN: 9780321758934

Intermediate Algebra for College Students | 6th Edition - Solutions by Chapter

Solutions by Chapter
4 5 0 288 Reviews
Textbook: Intermediate Algebra for College Students
Edition: 6
Author: Robert F. Blitzer
ISBN: 9780321758934

This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. This expansive textbook survival guide covers the following chapters: 74. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. The full step-by-step solution to problem in Intermediate Algebra for College Students were answered by , our top Math solution expert on 03/14/18, 07:37PM. Since problems from 74 chapters in Intermediate Algebra for College Students have been answered, more than 26192 students have viewed full step-by-step answer.

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

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

  • Column space C (A) =

    space of all combinations of the columns of A.

  • Condition number

    cond(A) = c(A) = IIAIlIIA-III = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

  • 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.

  • Dimension of vector space

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

  • Free columns of A.

    Columns without pivots; these are combinations of earlier columns.

  • Inverse matrix A-I.

    Square matrix with A-I A = I and AA-l = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B-1 A-I and (A-I)T. Cofactor formula (A-l)ij = Cji! detA.

  • Linearly dependent VI, ... , Vn.

    A combination other than all Ci = 0 gives L Ci Vi = O.

  • 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 .

  • 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.

  • Plane (or hyperplane) in Rn.

    Vectors x with aT x = O. Plane is perpendicular to a =1= O.

  • 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.

  • Rank one matrix A = uvT f=. O.

    Column and row spaces = lines cu and cv.

  • Rotation matrix

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

  • Schur complement S, D - C A -} B.

    Appears in block elimination on [~ g ].

  • Solvable system Ax = b.

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

  • Special solutions to As = O.

    One free variable is Si = 1, other free variables = o.

  • Spectral Theorem A = QAQT.

    Real symmetric A has real A'S and orthonormal q's.

  • Vector v in Rn.

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

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