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Textbooks / Math / College Mathematics for Business, Economics, Life Sciences, and Social Sciences 13

College Mathematics for Business, Economics, Life Sciences, and Social Sciences 13th Edition Solutions

Do I need to buy College Mathematics for Business, Economics, Life Sciences, and Social Sciences | 13th Edition to pass the class?

ISBN: 9780321945518

College Mathematics for Business, Economics, Life Sciences, and Social Sciences | 13th Edition - Solutions by Chapter

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72% of students who have bought this book said that they did not need the hard copy to pass the class. Were they right? Add what you think:

College Mathematics for Business, Economics, Life Sciences, and Social Sciences 13th Edition Student Assesment

Jay from Pennsylvania State University said

"If I knew then what I knew now I would not have bought the book. It was over priced and My professor only used it a few times."

Textbook: College Mathematics for Business, Economics, Life Sciences, and Social Sciences
Edition: 13
Author: Raymond A. Barnett; Michael R. Ziegler; Karl E. Byleen
ISBN: 9780321945518

This textbook survival guide was created for the textbook: College Mathematics for Business, Economics, Life Sciences, and Social Sciences, edition: 13. This expansive textbook survival guide covers the following chapters: 0. The full step-by-step solution to problem in College Mathematics for Business, Economics, Life Sciences, and Social Sciences were answered by , our top Math solution expert on 10/03/18, 06:29PM. College Mathematics for Business, Economics, Life Sciences, and Social Sciences was written by and is associated to the ISBN: 9780321945518. Since problems from 0 chapters in College Mathematics for Business, Economics, Life Sciences, and Social Sciences have been answered, more than 200 students have viewed full step-by-step answer.

Key Math Terms and definitions covered in this textbook
  • Augmented matrix [A b].

    Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

  • Big formula for n by n determinants.

    Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or - sign.

  • Cayley-Hamilton Theorem.

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

  • Commuting matrices AB = BA.

    If diagonalizable, they share n eigenvectors.

  • 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).

  • 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.

  • Distributive Law

    A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

  • Eigenvalue A and eigenvector x.

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

  • 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].

  • Hessenberg matrix H.

    Triangular matrix with one extra nonzero adjacent diagonal.

  • Linearly dependent VI, ... , Vn.

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

  • 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.

  • Network.

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

  • Orthogonal matrix Q.

    Square matrix with orthonormal columns, so QT = Q-l. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

  • 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.

  • 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.

  • Row picture of Ax = b.

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

  • Spanning set.

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

  • Subspace S of V.

    Any vector space inside V, including V and Z = {zero vector only}.

  • Volume of box.

    The rows (or the columns) of A generate a box with volume I det(A) I.

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