 4.1: The Heat Index HI , calculated from the air temperature and relativ...
 4.2: The monthly saving P that has to be deposit in a saving account tha...
 4.3: The growth of some bacteria populations can be described byN = Noek...
 4.4: The volume V and the surface area S of a torusshapedwater tube are ...
 4.5: A beam with a lengthL is attached to thewall with a cable as shown....
 4.6: Write a MATLAB program in a script file that calculate the average,...
 4.7: A rocket flying straight up measures the angle e withthe horizon at...
 4.8: Decay of radioactive materials can be modeled by the equation A = A...
 4.9: The monthly payment, P, of aN years mortgage of an amount L that wi...
 4.10: The balance of a loan, B, after n monthly payments is given byB = A...
 4.11: Early explorers often estimated altitude by measuring the temperatu...
 4.12: An isosceles triangle sign is designed to have atriangular printed ...
 4.13: A round billboard with radius R = 55 in. isdesigned to have a recta...
 4.14: student has a summer job as alifeguard at the beach. After spotting...
 4.15: An aiiplane is flying at a height of h = 900 ftwhile watching a tar...
 4.16: The stress intensity factor K at a cr I3J M crack in a beam exposed...
 4.17: The airplane shown is flying at a constant speed ofv = 50 mls in a ...
 4.18: The intrinsic electrical conductivity cr of a semiconductor can be ...
 4.19: The pressure drop l!.p in Pa for a fluidflowing in a pipe with a su...
 4.20: The net heat exchange by radiation from plate 1with radius b to pla...
 4.21: Given the coordinates ofthree points (x1,y1), (x2,J2) , and (x3,y3)...
 4.22: A truss is a structure made of membersjoined at their ends. For the...
 4.23: A truss is a structure made of membersjoined at their ends. For the...
 4.24: The graph of the function f{x) = ax3+ bx2+ex+ d passes through the ...
 4.25: The surface of many airfoils can bedescribed with an equation of th...
 4.26: During a golf match, a certain number of points are awarded for eac...
 4.27: The dissolution of copper sulfide in aqueous nitric acid is describ...
 4.28: The wind chill temperature, Twc, is the air temperature felt on exp...
 4.29: The stress intensity factor K at a crack is given byK = Co JM where...
Solutions for Chapter 4: Using Script Files and Managing Data
Full solutions for MATLAB: An Introduction with Applications  5th Edition
ISBN: 9781118629864
Solutions for Chapter 4: Using Script Files and Managing Data
Get Full SolutionsChapter 4: Using Script Files and Managing Data includes 29 full stepbystep solutions. Since 29 problems in chapter 4: Using Script Files and Managing Data have been answered, more than 4447 students have viewed full stepbystep solutions from this chapter. 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. This expansive textbook survival guide covers the following chapters and their solutions.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

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.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

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.

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