 6.1: Evaluate the following expressions without using MATLAB. Check thea...
 6.2: Given: a = 2 , b = 3 , c = 5 . Evaluate the following expressions ...
 6.3: Given: v = [4 1 2 3 1 2 5 0] and u = [ 5 1 0 3 3 2 1 5 ]. Evalu...
 6.4: Use the vectors v and u from 3. Use relational operators to create ...
 6.5: Evaluate the following expressions without using MATLAB. Check thea...
 6.6: Use loops to create a 3 x 5 matrix in which the value of each eleme...
 6.7: A symmetric (5 x 5) Pascal matrix is displayed on theright. Write a...
 6.8: The average monthly precipitation (in.) for Boston andSeattle durin...
 6.9: Write a program in a script file that fmds the smallest even intege...
 6.10: Fibonacci numbers are the numbers in a sequence in which the first ...
 6.11: The reciprocal Fibonacci constant v is defmed by the infinite sum: ...
 6.12: Write a program in a script file that determines the real roots of ...
 6.13: The value of 1t can be estimated by:Write a program (using a loop) ...
 6.14: The value of 1t can be estimated from the expression:=J2. JUJ2 . J2...
 6.15: Write a program that generates a vector with 20 random elements bet...
 6.16: Write a program that (a) generates a vector with 20 random integer ...
 6.17: Write a program that asks the user to input a vector of integers of...
 6.18: A vector is given by x = [4.5 5 16.12 21.8 10.1 10 16.11 5 14 3 ...
 6.19: The Pythagorean theorem states that a2 + b2 = c2 Write a MATLAB pro...
 6.20: A twin primes is a pair of prime numbers such that the difference b...
 6.21: An isolated prime is a prime number p such that neither p  2 nor p...
 6.22: A list of 30 exam scores is: 31, 70, 92, 5, 47, 88, 81, 73, 51, 76,...
 6.23: The Taylor series expansion for cos(x) is:x2 x4 x6 (1)n Zn cos(x) ...
 6.24: Write a MATLAB program in a script file that fmds a positive intege...
 6.25: The following are formulas for calculating the training heart rate ...
 6.26: Body Mass Index (BMJ) is a measure of obesity. In standard units, i...
 6.27: Write a program in a script file that calculates the cost of shippi...
 6.28: Write a program that determines the change given back to a customer...
 6.29: The concentration of a drug in the body C P can be modeled by the e...
 6.30: One numerical method for calculating the cubic root of a number, VP...
 6.31: Write a program in a script file that converts a measure of pressur...
 6.32: In a oneional random walk, the position x of a walker is computedby...
 6.33: The SieJp:inslci. triangle can be implemented in MAILAB by plotting...
 6.34: Cam is a mechanical device that transforms rotarymotion into linear...
 6.35: The overall grade in a course is determined from the grades of 6 qu...
 6.36: The handicap differential (HCD) for a round of golf is calculated f...
Solutions for Chapter 6: Programming in MATLAB
Full solutions for MATLAB: An Introduction with Applications  5th Edition
ISBN: 9781118629864
Solutions for Chapter 6: Programming in MATLAB
Get Full SolutionsThis textbook survival guide was created for the textbook: MATLAB: An Introduction with Applications, edition: 5. Since 36 problems in chapter 6: Programming in MATLAB have been answered, more than 4735 students have viewed full stepbystep solutions from this chapter. 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. Chapter 6: Programming in MATLAB includes 36 full stepbystep solutions.

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.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Column space C (A) =
space of all combinations of the columns of A.

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

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

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.

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

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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

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.

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

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

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.

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 .

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

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.

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

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.