 8.1: Plot the polynomial y = O.lx5 0.2x4x3 + 5x2 41.5x + 235 in the d...
 8.2: Plot the polynomial y = 0.008x41.8x25.4x + 54 in the domain14 :5...
 8.3: Use MATLAB to carry out the following multiplication of two polynom...
 8.4: Use MATLAB to carry out the following multiplication of polynomials...
 8.5: Divide the polynomial 10x620x5 + 9x4 + 10x3 + 8x2 + 11x3 by thep...
 8.6: Divide the polynomial0.24x7 + 1.6x6 + 1.5x57.41x4 1.8x34x2 75....
 8.7: The product of two consecutive integers is 6,972. Using MATLAB's bu...
 8.8: The product ofthree integers with spacing of 5 between them (e.g., ...
 8.9: A rectangular steel container has the outsidedimensions shown in th...
 8.10: An aluminum fuel tank has a cylindrical middlesection and a semisp...
 8.11: A 20 ftlong rod is cut into 12 pieces, which are weldedtogether to...
 8.12: A rectangular piece of cardboard, 40 in. long by 140 in. 1...
 8.13: Write a userdefmed function that adds or subtracts two polynomials...
 8.14: Write a userdefmed function that multiplies two polynomials. Name ...
 8.15: Write a userdefmed function that calculates the maximum (or minimu...
 8.16: A cone with base radius r and vertex in contactwith the surface of ...
 8.17: Consider the parabola y = 1.5 (x 3 )2 + 1 and the Ypoint P(3, 5.5)...
 8.18: The following data is given:X 2 5 6 8 9y 7 8 10 1 1 12X2 413 1514 1...
 8.19: The boiling temperature of water TB at various altitudes his given ...
 8.20: The U.S. population in selected years between 1815 and 1965 is list...
 8.21: The number of bacteria Ns measured at different times tis given in ...
 8.22: Growth data of a sunflower plant is given in the following table:We...
 8.23: Use the growth data from for the following:(a) Curvefit the data w...
 8.24: The following points are given:X 1 2.2 3.7 6.4 9 11.5 14.2 17.8 20....
 8.25: The standard air density, D (average of measurements made), at diff...
 8.26: Write a userdefmed function that fits data points to a power funct...
 8.27: Viscosity is a property of gases and fluids that characterizes thei...
 8.28: Measurements of the fuel efficiency of a car FE at various speeds v...
 8.29: The relationship between two variables P and t is known to be:p = m...
 8.30: When rubber is stretched, its elongation is initially proportional ...
 8.31: The yield strength, cry, of many metals depends on the size of the ...
 8.32: The transmission of light through a transparent solid can be descri...
 8.33: The ideal gas equation relates the volume, pressure, temperature, a...
Solutions for Chapter 8: Polynomials, Curve Fitting, and Interpolation
Full solutions for MATLAB: An Introduction with Applications  5th Edition
ISBN: 9781118629864
Solutions for Chapter 8: Polynomials, Curve Fitting, and Interpolation
Get Full SolutionsChapter 8: Polynomials, Curve Fitting, and Interpolation includes 33 full stepbystep solutions. This textbook survival guide was created for the textbook: MATLAB: An Introduction with Applications, edition: 5. MATLAB: An Introduction with Applications was written by and is associated to the ISBN: 9781118629864. Since 33 problems in chapter 8: Polynomials, Curve Fitting, and Interpolation have been answered, more than 4824 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

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).

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

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

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.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

GramSchmidt 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.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

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

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 •

Pseudoinverse A+ (MoorePenrose 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).

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)!

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

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