Question

Exercice 2. Let A given by -(iii) 21 A 1 -2 01 -2 1. Compate det( A) and ine.A) in MATLAB 2Use MATLAB to cheek boy coanpating ine(4)-A and A-inA) 3. Create two 5 x 5 matrices A and B with random entries between -30 and 20 by typing A-round(40 (rand3)-3) Bu40 (rands)-0. We will use these matrices to tind relationship between determinants Use MATLAB to fill the belom table det det (A det(A+B) (A) + det(B) det(AB) det(A det BTA (A (A det( B)/det(A det(B-AB) Look down your list and find any pains of expeessions that seem to have equal valans (for exampie,don det(A)-det(ATT). Do you think that the expresans you fond out to be equ wil be equal Ir ALL matricen? Try to find theorems in the book that confirm your obeervations, or try to detive them frot thoorens in your book Is it tae that det(A +B)de(A) + det(B)7

Answer 1

clc;
close all;
clear all;
A=[-2 1 0;1 -2 1;0 1 -2];
%%%%%%%%%%%%%%question 1%%%%%%%%%%%%%
fprintf('determinant of A=%f\n',det(A));
fprintf('inverse of A=\n');
%%%%%%%%%%%%%%question 2%%%%%%%%%%%%%
fprintf('inverse of A inverse\n');
A=inv(A)
fprintf('original A\n')
A=inv(A)
%%%%%%%%%%%%%%question 3%%%%%%%%%%%%%
fprintf('random matrix A\n');
A=round(40*(rand(5)-0.5))
fprintf('random matrix B\n');
B=round(40*(rand(5)-0.5))
det(A)
det(B)
det(3*A)
3*det(A)
3^3*det(A)
det(A')
det(B')
det(A+B)
det(A)+det(B)
det(A*B)
det(B*A)
det(A'*B')
det(B'*A')
det(inv(A))
1/det(A)
det(inv(A)*B)
det(A)/det(B)
det(B)/det(A)
det(inv(B)*A*B)
det(inv(B)*B)
det(2*inv(B)*B)

just copy this code and paste into a new script and run

you will get all values of table mention above
A I-2 1 0:1-2 1:0 1 -2] 몽몽몽몽몽몽몽몽몽몽몽몽용용ques tion 1몽몽몽몽몽몽몽몽몽몽몽몽용 fprintf ( determinant of A=%f\n", det (A) ) ; fprintf ('inverse of A n 용융융융융용융号号号号号号号question 2号号号号号号号号号号号号号 fprintf ('inverse of A inverseln' A-inv (A) fprintf ('original A\n') A-inv (A) 용용용용용용용용용용응용용용question 3용용용용용용용용용용용용용 fprintf ('random matrix A\n' A=round (40* (rand (5)-0.5)) fprintf ('random matrix B\n' B-r round (40* (rand (5) -0.5)) det (A) det (B) det (3 A) 3 det (A) 3 3 det (A) det (A') det (B') det (A+B) det (A) tdet (B) det (A*B) det (B A) det (A' *B') det (B' *A') det (inv (A)) 1/det (A) det (inv (A) *B) det (A)/det (B) det (B) /det (A) det (inv (B) A B

determinant of A4.000000 inver3e of A= nverse of A inverse -0.75000.5000 0.2500 -0.5000 1.0000 0.5000 -0.2500 0.5000 -0.7500 original A -2.0000 1.0000 1.0000 -2.0000 1.0000 1.0000 2.0000 random matrix A 20 -19 4-12 7 2 2 -15 -18 15 13 7 10 17 2 6 -16 7 2 random matrix B

random matrix B 12 10 12 -16 2 3 -16 -9 -16 7 -416 20 -13 2 13 -9 -12 ns -1.8313e+06 ans - 2243520 -4.4500e+08 -5.4938e+06 ans
serially on command window of matlab.