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Explorations in College Algebra 5th Edition - Solutions by Chapter

Explorations in College Algebra | 5th Edition | ISBN: 9780470466445 | Authors: Linda Almgren Kime

Full solutions for Explorations in College Algebra | 5th Edition

ISBN: 9780470466445

Explorations in College Algebra | 5th Edition | ISBN: 9780470466445 | Authors: Linda Almgren Kime

Explorations in College Algebra | 5th Edition - Solutions by Chapter

Explorations in College Algebra was written by Sieva Kozinsky and is associated to the ISBN: 9780470466445. This expansive textbook survival guide covers the following chapters: 9. This textbook survival guide was created for the textbook: Explorations in College Algebra, edition: 5. Since problems from 9 chapters in Explorations in College Algebra have been answered, more than 2421 students have viewed full step-by-step answer. The full step-by-step solution to problem in Explorations in College Algebra were answered by Sieva Kozinsky, our top Math solution expert on 12/23/17, 04:55PM.

Key Math Terms and definitions covered in this textbook
  • Adjacency matrix of a graph.

    Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

  • Column space C (A) =

    space of all combinations of the columns of A.

  • Commuting matrices AB = BA.

    If diagonalizable, they share n eigenvectors.

  • 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.

  • Diagonal matrix D.

    dij = 0 if i #- j. Block-diagonal: zero outside square blocks Du.

  • Hypercube matrix pl.

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

  • Kirchhoff's Laws.

    Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

  • Left inverse A+.

    If A has full column rank n, then A+ = (AT A)-I AT has A+ A = In.

  • Length II x II.

    Square root of x T x (Pythagoras in n dimensions).

  • 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).

  • Network.

    A directed graph that has constants Cl, ... , Cm associated with the edges.

  • 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.

  • Particular solution x p.

    Any solution to Ax = b; often x p has free variables = o.

  • 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.

  • Right inverse A+.

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

  • Schur complement S, D - C A -} B.

    Appears in block elimination on [~ g ].

  • Spectral Theorem A = QAQT.

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

  • Triangle inequality II u + v II < II u II + II v II.

    For matrix norms II A + B II < II A II + II B II·

  • Unitary matrix UH = U T = U-I.

    Orthonormal columns (complex analog of Q).

  • Vector addition.

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

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