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1 file:///c:/documents20and20settings/ravindra/desktop/html/exercis... 1 of 5 10/3/2008 3:17 PM Lab Exercise 2 - Matrices Hyd 510L, Fall, 2008, NM Tech Programmed by J.L. Wilson, Sept, 2008 Problem 2.1 Create a column vector in which the first element is 31, the elements decrease with increments of -4, and the last element is -9. ANS: Let's call this matrix C C = [31:-4:-9]' C = Problem 2.2 Create the matrix shown on the board in lab by using Matlab vector notation for creating vectors with constant spacing when entering the rows (i.e., do not enter the individual elements). ANS: Initialize the vector A=zeros(4,7); Fill the rows A(1,:)=linspace(0,6,7); A(2,:)=linspace(3,40,7); A(3,:)=linspace(28,26.5,7); A(4,:)=linspace(6,0,7); display(a) A = Problem 2.3 Create the matrix A of the preceding problem then use colons to

2 file:///c:/documents20and20settings/ravindra/desktop/html/exercis... 2 of 5 10/3/2008 3:17 PM address a range of elements to create the following vectors: (a) Create four-element row vector named va that contains the second through fifth elements of the third row of A. ANS: va=a(3,2:5) (b) Create a four-element column vector name vb that contains the elements of the sixth column of A. ANS: vb=a(:,6) va = vb = Problem 2.4 Give and demonstrate commands that... (a) find the largest and smallest elements of matrix A, ANS: maxvalue=max(max(a)) minvalue=min(min(a)) This sequentially finds the max(min)element of each column, forming a row vector and then the max(min)element of that vector. (b) add the elements of each row of A to yield a column vector of sums. ANS: define this vector to be vrowsum... Initialize the vector vrowsum=zeros(4,1); vrowsum(1)=sum(a(1,:)); vrowsum(2)=sum(a(2,:)); vrowsum(3)=sum(a(3,:)); vrowsum(4)=sum(a(4,:)); display(vrowsum) maxvalue = 40 minvalue = 0

3 file:///c:/documents20and20settings/ravindra/desktop/html/exercis... 3 of 5 10/3/2008 3:17 PM vrowsum = Problem 2.5 Create a matrix B with diagonal equal to +2 and the first off-diagonal equal to -1. ANS: no size specified; arbitrarily pick C to be 4x4 C=2*eye(4); creates a diagonal matrix of 2s Need the off-diagonals; assume "first off-diagonal" refers to both off-diagonals, above and below. There are short cuts for this, but they require loops (in the future). Instead... C(1,2)=-1; C(2,3)=-1; C(3,4)=-1 ; fill the upper off diagonal C(2,1)=C(1,2); C(3,2)=C(2,3); C(4,3)=C(3,4); fill lower using symmetry display(c) C = Problem 2.6 Discretize the function f=sin(xy)onto a uniform grid with spacing 0.1 in the x direction and 0.05 in the y direction (31*81= 2511 points). This simulates the results of a numerical code with these dimensions, spacings, and size. a. Create the x and y vectors using linspace or the colon command. ANS: assume that the left and bottom of the plot are x=0 and y=0 x=0:0.1:3.0; y=0:0.05:4.0; this and other answers not printed out here, they are big remove the ; to print or add a display command. b. Using matrix multiplication of the x and y vectors, create a matrix with the product of xiyj in the ijth entry. ANS: this is outer product, 4x1 times 1x4 yields 4x4 we do this by multiplying a col vector times a row vector M= y'*x; its important that y'x be used, and not x y' some checks, when used, should be (31,81),0,and 12 size(m) M(1,1)

4 file:///c:/documents20and20settings/ravindra/desktop/html/exercis... 4 of 5 10/3/2008 3:17 PM M(31,81) c. Calculate f=sin(xy) using the matrix you just created. ANS: F=sin(M); d. Contour the discrete results using the contour command. Use a maximum value of 1.0, a minimum of -1.0, and a contour interval of 0.2. Your contour map should have the correct geometry (3 x 4) and aspect ratio. Label the x and y axes, and include a plot title. arange for plots below to all show at the same time using subplot ANS: transform x,y to column vectors, and transform F subplot(1,3,1); [X,Y] = MESHGRID(x,y); [C,h]=contour(X,Y,F); axis equal; axis([ ]); xlabel('x'); ylabel('y'); title('d. contour plot of sin(xy)') Lable contour intervals (taken from help screen) set(h,'showtext','on','textstep',get(h,'levelstep')*2) e. Make a mesh of the results using the mesh command. Label the x, y, and z axes and include a plot title. Use the correct aspect ratio for the x and y axes. ANS: subplot(1,3,2);mesh(x,y,f); axis equal; xlabel('x'); ylabel('y'); zlabel('sin(xy)'); title('e. mesh plot of sin(xy)') f. Make a surface plot of the results using the surf command. Label the x, y, and z axes and include a plot title. Use the correct aspect ratio for the x and y ANS: subplot(1,3,3);surf(x,y,f); axis equal; xlabel('x'); ylabel('y'); zlabel('sin(xy)'); title('f. surface plot of sin(xy)') comment: in the past there was a significant difference in mesh and surface plots on all software, and the difference included available output devices (e.g., types of plotters). As you can see in these examples, the differences are no longer as important.

5 file:///c:/documents20and20settings/ravindra/desktop/html/exercis... 5 of 5 10/3/2008 3:17 PM Published with MATLAB 7.6