I can't see how you can hope to get unit length vectors b]without[/b] fractions. In fact, it is only because these numbers are chosen carefully that you don't get irrational numbers!
Question is attached. I just would like someone to verify whether the answer involves fractions/mixed numbers because I do tend to get antsy when I see them in my work. I wonder if I did it right.
So anyway here is what I got with Gram-Schmidt Process:
With x_{1}, x_{2}, and x_{3} representing the first, second, and third columns of A and v_{1}, v_{2}, and v_{3} representing each vector in the orthogonal basis respectively,
v_{1}= [1 2 0 2] v_{2} = [x_{2}] and v_{3}= [-1 7/6 1/6 -2/3]
Correct? And since we are on the topic, how do I go about finding the QR factorization of A ?
I can't see how you can hope to get unit length vectors b]without[/b] fractions. In fact, it is only because these numbers are chosen carefully that you don't get irrational numbers!
Hello,
This type of problem is part of a set of problems that try to avoid fractions. I know with gram-schmidt problems fractions tend to be inevitable but I was just wondering if I had done the problem correctly.
It's not asking for orthonormal, so you can construct an orthogonal basis that only involves whole numbers. I got the same v_{1} and v_{2} as you did but after scaling to whole number entries, I got [26 31 -75 -80]^{T} for v_{3}