PROBLEMS 2.1 What is the output when the following commands are 2.8 The command

Question

PROBLEMS 2.1 What is the output when the following commands are 2.8 The command 1inspace(a, b, n) generates a row vec- and b. Use colon tor of n equally spaced points between a notation to write an alternative onc-line command to gener- ate the same vector. Test your formulation for a-3,b A,3)-[1 A [A(:,1) [4 5 7] A(:,2)] A- sun(diag(A)) 2.2 You want to write MATLAB equations to compuie a (a) Write out the resulting matrix. vector of y values using the following equations 2.9 The following matrix is entered in MATLAB 3 2 1:0:0.5:1;inspace(6, 8, 3)] (b) Use colon notation to write a single-line MATLAB command to multiply the second row by the third col- umn and assign the result to the variable c. 8 sin(5r) (b) va4.a 2.10 The following equation can he used to compute values of y as a function of x where r is a vector. Make sure that you use periods only where necessary so the equation handles vector operations ybe properly. Extra periods will be considered incorrect. 2.3 Write a MATLAB expression to compute and dis- play the values of a vector of x values using the following equation sin(bx)(0.01 where a and b are parameters. Write the equation for imple- mentation with vector holding values from 0 to ?/2 in increments of Ax = x/40. Employ the minimum number of periods (G.e., dot no- tation) so that your formulation yields a vector for y. In ad- MATLAB, where a 2, b-5, and is a Assume that y and z are vector a and b are scalars quantities of equal length and dition, compute the vectior y where each element holds the square of each element of y. Combine x, y, and z into 2.4 What is displayed when the following MATLAB state- a matrix w, where each column holds one of the variables, ments are executed and display w using the short g format. In addition, gener- ate a labeled plot of y and z versus x. Include a legend on the plot (use help to understand how to do this). For y, use a 1.5-point, dashdotted red line with 14-point, red-edged, (a) A=[1 2; 3 4; 5 6]; A(2.). (c) a#2; b-8; c.4; a + b / c 2.5 The MATLAB humps function defines a curve that has white-faced pen 2 maxima (peaks) of unequal height over the interval0sas2, dard-sized (i.e., default) solid blue line with standard-sized, tagram-shaped markers. For z, use a stan- blue-edged, green-faced square markers. 2.11 A simple electric circuit consisting of a resistor, a ca- Cx-0.3)+0.0 0.9) +0.04 MATLAB to generate a plot of f(x) versus r with pacitor, and an inductor is depicted in Fig. P2.11. The charge x [0:1/256:2]; Use on the capacitor qlu) as a function of time can be computed as periods esperm the vectoropera ens needled to generate Do not use MATLAB's built-in humps function to gencrate the values of fx). Also, employ the minimum number of 40=wen?, cos Vi - LC fx) values for the plot. 2.6 Use the linspace function to create vectors identical to the following created with colon notation: (a) t# 4:635 (b) x=-42 2.7 Use colon notation to create vectors identical to the following created with the linspace function: where t- time, go the initial charge, R the resistance, L- inductance, and C= capacitance. Use MATLAB to generate a plot of this function from -0 to 0.8, given that go-10, R-60, L-9, and C 0.00005. 2.12 The standard normal probability density function is a bell-shaped curve that can be represented as (a) v=linspace(-2,1·5,8) (b) r= linspace(8,45,8)

Explanation / Answer

2.1 output is as follows.

A =

1 2 3
2 4 6
3 2 1

A =

1 2 3
2 4 2
3 6 1

A =

1 2
2 4
3 6

A =

1 4 2
2 5 4
3 7 6

A =

12

2.2 (a)

t=[1:.1:10];
y=(6*t.^3-3*t-4)./(8*sin(5*t));

"." is the periods used in the equation for vector operation.

2.2. (b)

t=[1:.1:10];
y=(6*t-4)./(8*t)-pi()*t/2;

2.3

y=[5:.1:10];
z=[5:.1:10];
a=5;
b=6;
x=(y.*(a+b*z).^1.8)./(z.*(1-y)) ;

2.4 (a)

ans =

3
4

2.4 (b)

y =

0
1.5000
3.0000
4.5000
6.0000

2.4 (c)

ans =

4

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