Recent content by aredian

yup that was it.. I missed the interval, so the xs turned out to be 1's thanks

L(ax+b) => \left[\begin{array}{cc}x&x^2 / 2 \\0&1\end{array}\right] [\begin{array}{c}\ \alpha\\ \beta \end{array} \right]

Homework Statement If L( p(x) ) = [ integral (p(x)) dx , p(0) ] find representation matrix A such that L (a + bx) = A[a b]^T Homework Equations The Attempt at a Solution I don't quite understand the question. I think that: if the base from p2 is {1, x} then any...

You guys are the best! Thank you very much!

In my notes I have L(x)=(r*cos(a+t) , r*sin(a+t)). I though they would be the same so I reduced it to 2*a. So I can graph a point P as you described it, anywhere and then increase the angle by a to prove my point? No need to figure out where exactly r*cos(a) or r*sin(a) will actually be located?

is it a counter clock wise rotation by a, to whatever the line is?

well... Obiously the a was doubled. But if the polar coordinates are of the form (r, a), How should I graph ( r cos 2a , r sin 2a )? :S

If they stay the same which I guess so... then by the properties of trigonometric functions... L(x) in polar coord will be [ (r cos 2a) , (r sin 2a) ] ?

Homework Statement Let L(x) be the Linear operator in R^2 defined by L(x) = (x1 cos a - x2 sin a, x1 sin a + x2 cos a)^T Express x1, x2 & L(x) in terms of Polar coordinates. Describe geometrically the effects of the L.T. Homework Equations Well I know that: a = tan^-1 (x2 / x1)...

Yes indeed and the base is of the form {x^2-1, x-1} Thanks!

Ok... since c = -a -b I can use ax^2 + bx + (-a -b)1. Correct? This would yield the vectors of the form (a, b, -(a+b)) and their lineal combination would be of the form a(1,0,-1)^T + b(0,1,-1)^T = (x^2, x, 1). The coeff matrix is non singular so they are LI. However something is wrong with...

Great! Now for T... Are the vectors of T (p(1) = 0) of the form (a, b, -(a+b)) ? grouping well x^2, x, 1 Im not sure about the vectors in S \capT. Are they of the form (a, b, c) for c=0 or only (a, b)? Thanks for your help!

Since the vectors are of the type (a, b, 0) grouping by x^2, x, 1 then taking a linear combination of these, I can tell a(1,0,0)^T + b(0,1,0) = (x^2, x, 1) and use it to determine if they span S. They DO!. On the other hand the coeff matriz [(1,0,0)^T (0,1,0)^T] is non singular so these vectors...

OK... Now I am a bit more confused. Does that means the vectors in p(0) = 0 grouped by the powers of X would be of the form (0 0 1)^{T}? If so, then I take say 2 vectors, A and B, and need to verify they are L.I. and if they span S in order to declare them a basis of S. How do I get a...

Homework Statement Let S be the subspace P3 consisting of all polynomials P(x) such that p(0) = 0, and let T be the subspace of all polynomials q(x) such that q(1) = 0. Find a basis for S, T and S\capT Homework Equations The Attempt at a Solution I know that a basis is formed by...