 3.1: For the function y = x2 e05x +x , calculateth e value of y for the...
 3.2: For the function y = (x + 25)3 , calculate the value of y for the f...
 3.3: For the function y = (x + 7j , calculate the value of y for the fol...
 3.4: For the funct10n y = . 2 , calculate the value of y for the followm...
 3.5: The radius, r, of a sphere can be calculated from its surface area,...
 3.6: The electric field intensity, E(z), due to a ringof radius R at any...
 3.7: The voltage Vc(t) (in V) and the current i(t)(in Amp) t seconds aft...
 3.8: The length lui (magnitude) of a vector u = xi+ yj + zk is given byl...
 3.9: A vector wL of length Lin the direction of a vector u = xi+ yj + zk...
 3.10: The following two vectors are defmed in MATLAB:v = [15,8,6] u = [3...
 3.11: Two vectors are given:u = 5i 6j+9k and v = 11i+7j 4kUse MATLAB to...
 3.12: Defme the vector v = [2 3 4 5 6]. Then use the vector in a mathemat...
 3.13: Define the vector v = [ 8 6 4 2] . Then use the vector in a mathema...
 3.14: Define x andy as the vectors x = [1, 2, 3, 4, 5] and y = [2, 4, 6, ...
 3.15: Define r and s as scalars r = 1.6 x 103 and s = 14.2 , and, t, x, a...
 3.16: The area of a triangle ABC can be calculated bylrAB x rAd/2, where ...
 3.17: The volume of the parallelepiped shown can becalculated by r0B (r0A...
 3.18: Define the vectors:u = Sl2j +4k, v = 21+ 7J +3k, and w = 81 + lj ...
 3.19: The dot product can be used for determining theangle between two ve...
 3.20: Use MAILAB to show that the angle inscribedin a semicircle is a ri...
 3.21: The position as a function of time (x(t),y(t)) yof a projectile fir...
 3.22: Use MATLAB to show that the sum of the infinite series I 2 converge...
 3.23: Use MATLAB to show that the sum of the infmite series I <9110)n con...
 3.24: According to Zeno's paradox any object in motion must arrive at the...
 3.25: Show that lim cos(2x) 1 = 4 .x70 cosx1Do this by first creating ...
 3.26: Show that bm  4= . x7Ixll4_1 3Do this by first creating a vecto...
 3.27: The demand for water during a fire is often the most important fact...
 3.28: The ideal gas equation states that P = nT, where P is the pressure,...
 3.29: Create the following three matrices:[ 1 3 5 A= 2 2 42 0 6B= [0 2...
 3.30: Use the matrices A, B, and C from the previous problem to answer th...
 3.31: Create a 4 x 4 matrix A having random integer values between 1 and ...
 3.32: The magic square is an arrangement of numbers in a square grid in s...
 3.33: Solve the following system of three linear equations: 4x+3y+z = 1...
 3.34: Solve the following system of five linear equations:2.5ab+3c+ 1.5d...
 3.35: A food company manufactures five types of 8 oz Trail mix packages u...
 3.36: The electrical circuit shown consists of resistorsand voltage sourc...
 3.37: The electrical circuit shown consists ofresistors and voltage sourc...
Solutions for Chapter 3: Mathematical Operations with Arrays
Full solutions for MATLAB: An Introduction with Applications  5th Edition
ISBN: 9781118629864
Solutions for Chapter 3: Mathematical Operations with Arrays
Get Full SolutionsChapter 3: Mathematical Operations with Arrays includes 37 full stepbystep solutions. 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. Since 37 problems in chapter 3: Mathematical Operations with Arrays have been answered, more than 4474 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.

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

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

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

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

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

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.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

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

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

Iterative method.
A sequence of steps intended to approach the desired solution.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)ยท(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 .

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

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

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.