Question 1: Solve the system of equations -w + 3x - 2y + z = 1 w + 2x - 4y - 3z = 2 x + 2y + z = 4 2w + 3x - y - z = 7 The attempt at a solution To do this in matlab, this is what I will did: >> A=[-1,3,-2,1;1,2,-4,-3;0,1,2,1;2,3,-1,-1]; b = [1;2;4;7] >>x=inv(A)*b Then matlab should give an answer with the solutions of w, x, y and z written in a separate line…no? Question 2: Find the eigenvalues and eigenvectors of the matrix 3, -1, 0, 0 -1, 5, -2, 0 0, -2, 6, -1 0, 0, -1, 2 The attempt at a solution In matlab do I do this: >>A=[3,-1,0,0;-1,5,-2,0;0,-2,6,-1;0,0,-1,2] ; >>[V,D]=eig(A) Then I should get an answer for V and D, and v is a matrix whose columns are the eigenvectors and D is the diagonal matrix, so we multiply the first column of V with the first diagonal of D etc… am I wrong? Question 3: Let A= -3, 4, 2, 0 1, -2, 0, 1 -4, 5, 0, 3 0, 1, -4, 2 Write the Matlab commands to construct the following matrix: 3, 0, 0, 0, -3, 1, -4, 0 0, 4, 0, 0, 4, -2, 5, 1 0, 0, 5, 0, 2, 0, 0, -4 0, 0, 0, 6, 0, 1, 3, 2 -3, 4, 2, 0, 5, 5, 5, 5 1, -2, 0, 1, 5, 5, 5, 5 -4, 5, 0, 3, 5, 5, 5, 5 0, 1, -4, 2, 5, 5, 5, 5 The attempt at a solution In matlab should i do this: >>A=[-3,4,2,0;1,-2,0,1;-4,5,0,3;0,1,-4,2] Then to construct the other big matrix do I do this: >> B=[diag(3:6),A’;A, fives(4,4)] You’ve probably all figured that I don’t have access to matlab just now, so I would be grateful if someone who has access to matlab could just copy and paste the commands in to see if it works. Also between each question do I write clear all to clear everything before I start the question?
For question 2, you don't have to do anything after eig. D is a diagonal matrix of eigenvalues - just read them off the diagonal, and V is the corresponding matrix of eigenvectors - just take each column separately. (You also have the relationship A*V=V*D - this is what you may be thinking when you want to multiply...?) Qu 3 is right but for, there is no such thing as fives: use 5*ones(4,4). Qu 1 looks good too.
ok thanx i really appreciate your help! and you didn't have to say 'there is no such thing' just correct me lol