Find the QR Factorization of a matrix

[badvash88]

Homework Statement

Find the QR factorization for the 4x3 matrix M
1 1 0
1 0 2
1 0 1
1 1 1

Homework Equations

M = QR

The Attempt at a Solution

I got the first two columns of Q correct, but I am getting the third wrong for some reason beyond me.
for Q, i got u₁= 1/2 (1, 1, 1, 1) (vertical, not horizontal)
and u₂ = 1/2 (1, -1, -1, 1) (once again vertical, not horizontal, don't know how to make matrices easily on here)
I got R correct except for the last number in the bottom right, need v₃perp.thanks

 

[badvash88]

anyone?

 

[cronxeh]

Q=[-0.5 0.5 -0.5 -0.5; -0.5 -0.5 0.5 -0.5; -0.5 -0.5 -0.5 0.5; -0.5 0.5 0.5 0.5]
r=[-2 -1 -2; 0 1 -1; 0 0 1; 0 0 0]

 

[badvash88]

your matrices answers seem to big. there should only be three columns in Q

are you sure those are right. i got the answer not the solution and my u1 and u2 are the same as that, but its my u3 that is wrong. it says it is (-3/2, 3/2, 1/2, 1/2)

 

[cronxeh]

Before we decide to correct my work, let's multiply Q and R, something you could've done with your Q and R to see your mistake


>> [-0.5 0.5 -0.5 -0.5; -0.5 -0.5 0.5 -0.5; -0.5 -0.5 -0.5 0.5; -0.5 0.5 0.5 0.5]*[-2 -1 -2; 0 1 -1; 0 0 1; 0 0 0]

ans =

1 1 0
1 0 2
1 0 1
1 1 1

 

[badvash88]

ahh but you are wrong. you have TOO MANY columns. there are only three columns in Q and you just added a row in R to make M work.
i just figure my solution is correct and the soltion book is wrong
Q is
.5 .5 -.5
.5 -.5 .5
.5 -.5 -.5
.5 .5 .5

R is
2 1 2
0 1 -1
0 0 1

that equals M
so i believe that is right.
thanks anyways tho

 

[cronxeh]

Ok then..

 

[hgfalling]

You know that Q is supposed to be an orthogonal matrix, right? So if your Q isn't square, you've done something wrong.

 

[badvash88]

nah man. Q is fine. R is the orthogonal matrix i believe. or at least it is always squared
my professor and another solution book both verified my answer.

thanks you guys, but this problem is good
/thread

 

[Tedjn]

I haven't checked your solution, but no, Q is the orthogonal matrix... so it needs to be 4 by 4.