Make $16/hr - and build your resume - as a Marketing Coordinator! Apply Now
> > Elementary and Intermediate Algebra 5

Elementary and Intermediate Algebra 5th Edition - Solutions by Chapter

Elementary and Intermediate Algebra | 5th Edition | ISBN: 9781111567682 | Authors: Alan S. Tussy R. David Gustafson

Full solutions for Elementary and Intermediate Algebra | 5th Edition

ISBN: 9781111567682

Elementary and Intermediate Algebra | 5th Edition | ISBN: 9781111567682 | Authors: Alan S. Tussy R. David Gustafson

Elementary and Intermediate Algebra | 5th Edition - Solutions by Chapter

Elementary and Intermediate Algebra was written by Patricia and is associated to the ISBN: 9781111567682. This textbook survival guide was created for the textbook: Elementary and Intermediate Algebra, edition: 5. The full step-by-step solution to problem in Elementary and Intermediate Algebra were answered by Patricia, our top Math solution expert on 01/24/18, 03:12PM. Since problems from 14 chapters in Elementary and Intermediate Algebra have been answered, more than 9823 students have viewed full step-by-step answer. This expansive textbook survival guide covers the following chapters: 14.

Key Math Terms and definitions covered in this textbook
  • Associative Law (AB)C = A(BC).

    Parentheses can be removed to leave ABC.

  • 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).

  • 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

  • Exponential eAt = I + At + (At)2 12! + ...

    has derivative AeAt; eAt u(O) solves u' = Au.

  • Gram-Schmidt orthogonalization A = QR.

    Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

  • Hankel matrix H.

    Constant along each antidiagonal; hij depends on i + j.

  • Independent vectors VI, .. " vk.

    No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

  • Krylov subspace Kj(A, b).

    The subspace spanned by b, Ab, ... , Aj-Ib. Numerical methods approximate A -I b by x j with residual b - Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

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

    Vector addition and scalar multiplication.

  • 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).

  • Orthonormal vectors q 1 , ... , q n·

    Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q -1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

  • Plane (or hyperplane) in Rn.

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

  • Row picture of Ax = b.

    Each equation gives a plane in Rn; the planes intersect at x.

  • Schur complement S, D - C A -} B.

    Appears in block elimination on [~ g ].

  • Singular matrix A.

    A square matrix that has no inverse: det(A) = o.

  • Skew-symmetric matrix K.

    The transpose is -K, since Kij = -Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

  • 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.

  • Transpose matrix AT.

    Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and A-I are BT AT and (AT)-I.

  • 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·

×
Log in to StudySoup
Get Full Access to Elementary and Intermediate Algebra

Forgot password? Reset password here

Join StudySoup for FREE
Get Full Access to Elementary and Intermediate Algebra
Join with Email
Already have an account? Login here
Forgot password? Reset your password here

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
Sign up
We're here to help

Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com

Got it, thanks!
Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Got it, thanks!
Already have an Account? Is already in use
Log in
Incorrect Password The password used to log in with this account is incorrect
Try Again

Forgot password? Reset it here