 Chapter 1: Starting with MATLAB
 Chapter 10: ThreeDimensional Plots
 Chapter 11: Symbolic Math All
 Chapter 2: Creating Arrays
 Chapter 3: Mathematical Operations with Arrays
 Chapter 4: Using Script Files and Managing Data
 Chapter 5: TwoDimensional Plots
 Chapter 6: Programming in MATLAB
 Chapter 7: UserDefined Functions and Function Files
 Chapter 8: Polynomials, Curve Fitting, and Interpolation
 Chapter 9: Applications in Numerical Analysis Numerical
MATLAB: An Introduction with Applications 5th Edition  Solutions by Chapter
Full solutions for MATLAB: An Introduction with Applications  5th Edition
ISBN: 9781118629864
MATLAB: An Introduction with Applications  5th Edition  Solutions by Chapter
Get Full SolutionsThis expansive textbook survival guide covers the following chapters: 11. The full stepbystep solution to problem in MATLAB: An Introduction with Applications were answered by , our top Math solution expert on 03/15/18, 06:08PM. MATLAB: An Introduction with Applications was written by and is associated to the ISBN: 9781118629864. This textbook survival guide was created for the textbook: MATLAB: An Introduction with Applications, edition: 5. Since problems from 11 chapters in MATLAB: An Introduction with Applications have been answered, more than 969 students have viewed full stepbystep answer.

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

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Condition number
cond(A) = c(A) = IIAIlIIAIII = 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.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

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

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

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 •

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.
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