Consider the 4x4 matrices
A =
(1 2 3 4)
(5 6 7 8)
(9 10 11 12)
(13 14 15 16)B=
(1 2 3 4)
(8 5 6 7)
(11 12 9 10)
(14 15 16 13)
The question I was asked was the following: Show that there does not exist an endomorphism f: ℝ4 -> ℝ4 and basis 'a' and 'b' of R^4, such that A = a[f]a and B=b[f]b...
ok - taking a=b=c=d=1. our basis would be:{1,x,x3+x2}
I am not sure where this is going? the question asked for a basis consisting of 4 vectors.
Would an alternative method to show that we have a basis be the following:
Take {1,x,x3+x2,x3} which is linear independant.
Now we have...
Nice. Can't believe I didn't see that. It is clearly linearly independant. Is it enough to say that since \{1,x,x^3+x^2,x^3\} is a linear combination of pi that it will span the vector space?
Thanks
Homework Statement
Can you find a basis {p1, p2, p3, p4} for the vector space ℝ[x]<4 s.t. there does NOT exist any polynomials pi of degree 2? Justify fully.Homework Equations
The Attempt at a Solution
We know a basis must be linearly independant and must span ℝ[x]<4. So intuitively if there...
Thanks for your reply.
If I were to take the transpose so it becomes:
({1,2,3,4},{2,3,4,5},{3,4,5,1},{4,5,1,2}, {5,1,2,3})
Would you see any quick way to determine linear independance?
Many thanks
Hi,
I was wondering what the quickest set of vectors in higher dimensions, say ℂ5?
I have a set of vectors { (1,2,3,4,5), (2,3,4,5,1), (3,4,5,1,2), (4,5,1,2,3) }
Clearly this is linearly dependant but how could I justify this quickly?
What are the quickest ways to determine if this is...
[/itex]Homework Statement
Is the following statement true or false: 'if (cn) and (dn) are bounded sequences of positive real numbers then:
lim sup (cndn) = (lim sup cn)(lim sup dn)Homework Equations
The Attempt at a Solution
for all n in the positive reals. cn and dn are bounded.
Since cn...
Homework Statement
Let F = ( -y/(x2+y2) , x/(x2+y2) ) Show that this vector field is irrotational on ℝ2 - {0}, the real plane less the origin. Then calculate directly the line integral of F around a circle of radius 1.Homework Equations
The Attempt at a Solution
To show F is irrotational we...
Yeah forget about the 'f's.. yeah that makes sense.
Deveno, if I sent you the question sheet it may be easier for both you and I to understand. Of course, only if you are happy to help. Would that be okay? The reason I ask is that it is hard for me to get my points across since I don't know...
Oh okay. If we take y=0 (using the condition 0€M)
Then we get (lambda)x + (1-lambda)(0) which is just (lambda)x
So we know for any x and lambda that it will be in M. So that is iii done.
What about ii
Ps: I'm on my phone so sorry for weak notation.
Thanks micro