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Algebra and Trigonometry 9th Edition - Solutions by Chapter

Algebra and Trigonometry | 9th Edition | ISBN: 9780321716569 | Authors: Michael Sullivan

Full solutions for Algebra and Trigonometry | 9th Edition

ISBN: 9780321716569

Algebra and Trigonometry | 9th Edition | ISBN: 9780321716569 | Authors: Michael Sullivan

Algebra and Trigonometry | 9th Edition - Solutions by Chapter

Solutions by Chapter
4 5 0 341 Reviews
Textbook: Algebra and Trigonometry
Edition: 9
Author: Michael Sullivan
ISBN: 9780321716569

This expansive textbook survival guide covers the following chapters: 107. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. The full step-by-step solution to problem in Algebra and Trigonometry were answered by Sieva Kozinsky, our top Math solution expert on 12/23/17, 05:02PM. Since problems from 107 chapters in Algebra and Trigonometry have been answered, more than 17862 students have viewed full step-by-step answer. Algebra and Trigonometry was written by Sieva Kozinsky and is associated to the ISBN: 9780321716569.

Key Math Terms and definitions covered in this textbook
  • Back substitution.

    Upper triangular systems are solved in reverse order Xn to Xl.

  • Column picture of Ax = b.

    The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

  • 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.

  • Elimination matrix = Elementary matrix Eij.

    The identity matrix with an extra -eij in the i, j entry (i #- j). Then Eij A subtracts eij times row j of A from row i.

  • Elimination.

    A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

  • 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.

  • Left inverse A+.

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

  • Lucas numbers

    Ln = 2,J, 3, 4, ... satisfy Ln = L n- l +Ln- 2 = A1 +A~, with AI, A2 = (1 ± -/5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

  • Minimal polynomial of A.

    The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A - AI) if no eigenvalues are repeated; always meA) divides peA).

  • Nullspace matrix N.

    The columns of N are the n - r special solutions to As = O.

  • Outer product uv T

    = column times row = rank one matrix.

  • Particular solution x p.

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

  • Polar decomposition A = Q H.

    Orthogonal Q times positive (semi)definite H.

  • Projection p = a(aTblaTa) onto the line through a.

    P = aaT laTa has rank l.

  • Pseudoinverse A+ (Moore-Penrose inverse).

    The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

  • Reduced row echelon form R = rref(A).

    Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

  • Special solutions to As = O.

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

  • Vector v in Rn.

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

  • Wavelets Wjk(t).

    Stretch and shift the time axis to create Wjk(t) = woo(2j t - k).

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