Question

MATLAB HELP!!! Recall that if A is an m × n matrix and B is a p × q matrix, then the product C = AB is defined if and only if n = p, in which case C is an m × q matrix.

5. Recall that if A is an mx n matrix and B is a px q matrix, then the product C-AB is defined if and only if n = p, in which case C is an m x q matrix. (a) Write a function M-file that takes as input two matrices A and B, and as output produces the product by columns of the two matrix. For instance, if A is 3 x 4 and B is 4 x 5, the product is given by the matrix [A#8( : , 1) , Ae( : ,2) , A#8( : ,3) , A*B( : ,4) , A*B( : ,5)] c HIS CONTEN MAY 019 v2 Copyright& School of Matbematical and Statistical Sclencex, Arisona State University T IS PROTECTED AND SOLD OF The function file should work for any dimension of A and B and it should perform a check to see if the dimensions match (Hint: use a for loop to define each column of C). Call the file columnproduct._. Test your function on a random 4x 3 matrix A and a random 3x 6 matrix B. Compare the output with A B 6 Repeat with 5 x 5 and 5 × 2 matrices and with 5 x 5 and 2 × 5 matrices. Use the command rand to generate the random matrices for testing Include in your lab report the function M-file and the output obtained by running it. (b) Write a function M-file that takes as input two matrices A and B, and as output produces the product by rors of the two matrices. For instance, if A is 3 x 4 and B is 4 x 5, the product AB is given by the matrix The function file should work for any dimension of A and B and it should perform a check to see if the dimensions match (Hint: use a for loop to define each row of c). Call the file rouproduct. Test your function on a random 4x 3 matrix A and a random 3x 6 matrix B. Compare the output with A B 6 Repeat with 5 x 5 and 5 × 2 matrices and with 5 x 5 and 2 × 5 matrices. Use the command rand to generate the random matrices for testing Include in your lab report the function M-file and the output obtained by running it.

Answer 1

%%Matlab code for row product and column product clear all close all Rnadom matrix A(4X3) and B(3X6) and their product A-rand (4,3); B-rand (3,6)i fprintf( 'Matrix product using function columnproductln') disp (columnproduct (A, B)) fprintf( Matrix product using matrix multiplication n) disp (A*B) Rnadom matrix A (5X5) and B(5X2) and their product A-rand (5,5); B-rand (5,2); fprintf ( Matrix product using function columnproduct\n) disp (columnproduct (A,B)) fprintf ( 'Matrix product using matrix multiplication\n') disp(A*B) Rnadom matrix A (5X5) and B (2X5) and their product A-rand (5,5); B-rand (2,5) Eprintf 'Matrix product using function columnproduct\n' ) disp (columnproduct (A, B)) fprintf 'Matrix product using matrix multiplication n') %d is p (A* B) %Rnadom matrix A(4x3) A-rand (4,3); and B(3x6) and their product B-rand (3,6); fprintf ( Matrix product using function rowproduct\n') disp (rowproduct(A, B)) fprintf ( 'Matrix product using matrix multiplication n) disp(A*B) Rnadom matrix A(5X5) and B(5X2) and their product A-rand (5,5); B-rand (5,2); fprintf( Matrix product using function rowproductin') disp (rowproduct (A, B)) fprintf( 'Matrix product using matrix multiplication\n') disp (A*B) Rnadom matrix A (5X5) and B(2X5 and their product A-rand (5,5); B-rand (2,5);

fprintf( 'Matrix product using function rowproduct\n) disp (rowproduct(A, B)) fprintf( 'Matrix product using matrix multiplication\n') disp (A B) %%Function for columnproduct function C- columnproduct (A, B) sz1-size (B); sz2-size (A); if sz1(1)z2 (2) msg = 'Matrix dimension mismatched' ; error (msg) else for i-1: sz1(2) end end 8888%옹88%옹88888888888888888888옹%88%%88옹옹88옹옹% %%Function for rowproduct function C- rowproduct (A,B) szl-size (A); sz2-size (B); if szl ( 2 )-=sz2 ( 1) msgMatrix dimension mismatched error (msg) else for i-l:sz1(1) end 용号号응용号号응용号号%%号号%%号 End of Code 욤욤융융욤욤융융욤욤융융욤욤융융 Matrix product using function columnproduct Columns 1 through 3 1. 13356265073902 0.908250645593387 1.41014405790332 0.426373200891699 0.443399900009631 0.53511209858212 1.14573209609746 0.813750550533468 I.60751376038817

1.33241071963862 1. 13727405296105 1.81266282325218 Columns 4 through 6 1. 05603130257273 0.646900764769298 1.0216568678775 0.154638199032551 0.423426621843155 0.32344694699612 1. 35914495314464 1.08947861176892 1.43788809399847 1.51803382401491 0.979694976736505 1.43776623165306 Matrix product using matrix multiplication Columns 1 through 3 1. 13356265073902 0.908250645593387 1.41014405790332 0.426373200891699 0.443399900009631 0.53511209858212 1. 14573209609746 0.813750550533468 1.60751376038817 1. 33241071963862 1.13727405296105 1.81266282325218 Columns 4 through 6 1.0560313025 7273 0.646900764769298 1.0216568678775 0.154638199032551 0.423426621843155 0.32344694699612 1.35914495314464 1.08947861176892 1.43788809399847 1.51803382401491 0.979694976736505 1.43776623165306 Matrix product using function columnproduct 1. 27430486396535 1.3793228548448 1.23776967887651 1.89931119244429 0.8744351 75588595 1. 19953141025844 1.31196023953442 1.5847227911665 1. 15497401338641 1.41652993554949 Matrix product using matrix multiplication 1.27430486396535 1.3793228548448 1. 23776967887651 1. 89931119244429 0.874435175588595 1. 19953141025844 1. 31196023953442 1.5847227911665 1.15497401338641 1.41652993554949 Matrix product using function rowproduct Columns 1 through 3

0.648520298409864 1.05981624033438 1.38143507866166 0.60660413566284 1. 18592768274163 1.22803803148928 0.704904710778998 1.20933057892277 1.34354385526094 0.398723495125062 0.781334817858008 0.868932017117911 Columns 4 through 6 0. 60205872136353 0.625220664630926 0.811257360338055 0.597712010753689 0.797380770893582 0.742848567943035 0.646461799692862 0.669996932284395 0.890493793087342 0.401327618120531 0.558486721723425 0.482117475658411 Matrix product using matrix multiplication Columns 1 through 3 0.648520298409864 1.05981624033438 1.38143507866166 0. 60660413566284 1. 18592768274163 1.22803803148928 1.20933057892277 0.704904710778998 1.34354385526094 0.398723495125062 0.781334817858008 0.868932017117911 Columns 4 through 6 0.625220664630926 0. 60205872136353 0.811257360338055 0.597712010753689 0.797380770893582 0.742848567943035 0.646461799692862 0.669996932284395 0.890493793087342 0.401327618120531 0.558486721723425 0.482117475658411 Matrix product using function rowproduct 1.50136315038211 1. 46624030096342 1.50487535739117 1. 73863797389699 0.999636388936932 0.649550700486462 0.353072108487477 0.431430581877311 1.02218005330407 1.24158957480378 Matrix product using matrix multiplication 1.46624030096342 1.50136315038211 1.73863797389698 1.50487535739117 0.999636388936932 0.649550700486462

0.353072108487477 0.431430581877311 1.02218005330407 1. 24158957480378 Matrix product using function rowproduct Error using matt pro rowproduct (line 85) Matrix dimension mismatched Error in matt_pro (line 55) disp (rowproduct (A, B) ) Published with MATLABE R2018a

%%Matlab code for row product and column product
clear all
close all
%Rnadom matrix A(4X3) and B(3X6) and their product
A=rand(4,3);
B=rand(3,6);

fprintf('Matrix product using function columnproduct\n')
disp(columnproduct(A,B))
fprintf('Matrix product using matrix multiplication\n')
disp(A*B)

%Rnadom matrix A(5X5) and B(5X2) and their product
A=rand(5,5);
B=rand(5,2);

fprintf('Matrix product using function columnproduct\n')
disp(columnproduct(A,B))
fprintf('Matrix product using matrix multiplication\n')
disp(A*B)

%Rnadom matrix A(5X5) and B(2X5) and their product
A=rand(5,5);
B=rand(2,5);

%fprintf('Matrix product using function columnproduct\n')
%disp(columnproduct(A,B))
%fprintf('Matrix product using matrix multiplication\n')
%disp(A*B)

%Rnadom matrix A(4X3) and B(3X6) and their product
A=rand(4,3);
B=rand(3,6);

fprintf('Matrix product using function rowproduct\n')
disp(rowproduct(A,B))
fprintf('Matrix product using matrix multiplication\n')
disp(A*B)

%Rnadom matrix A(5X5) and B(5X2) and their product
A=rand(5,5);
B=rand(5,2);

fprintf('Matrix product using function rowproduct\n')
disp(rowproduct(A,B))
fprintf('Matrix product using matrix multiplication\n')
disp(A*B)

%Rnadom matrix A(5X5) and B(2X5) and their product
A=rand(5,5);
B=rand(2,5);

fprintf('Matrix product using function rowproduct\n')
disp(rowproduct(A,B))
fprintf('Matrix product using matrix multiplication\n')
disp(A*B)

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%Function for Columnproduct
function C= columnproduct(A,B)

    sz1=size(B);
    sz2=size(A);
    if sz1(1)~=sz2(2)
        msg = 'Matrix dimension mismatched';
        error(msg)
    else
        for i=1:sz1(2)
            C(:,i)=A*B(:,i);
        end
    end
  
end
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%Function for rowproduct
function C= rowproduct(A,B)
    sz1=size(A);
    sz2=size(B);
  
    if sz1(2)~=sz2(1)
        msg = 'Matrix dimension mismatched';
        error(msg)
    else
        for i=1:sz1(1)
            C(i,:)=A(i,:)*B;
        end
    end
  
end

    %%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%