Recent content by SetepenSeth

I think I'll start from scratch cause I don't follow

Homework Statement Consider a conductor wire with a charge Q uniformly distributed, shaped in the form of an arc of radius R and amplitude 2A (were A is a given number between 0 and π). Find the value of the electric field in the center of the arc. Homework Equations ##E(P)= \int K_e...

Thank you both. Indeed my problem is that I was missing the step to write the vectors in terms of Ci basis. However I've found I have a conceptual mistake in my question. Apparently, a transition matrix is completely different from a matrix associated to a transformation, and it was the later...

Homework Statement Find the transition matrix ##P## of a transformation defined as ##T:ℝ_2→ℝ_3## ##T:\begin{bmatrix}a\\b\end{bmatrix} = \begin{bmatrix}a+2b\\-a\\b\end{bmatrix}## For basis ##B=\begin{bmatrix}1\\2\end{bmatrix},\begin{bmatrix}3\\-1\end{bmatrix}##...

Thank you both, now it all makes sense.

I see, I just noticed I followed a wrong assumption ##V= a\begin{bmatrix} 1&0\\ 0&0 \end{bmatrix}+ b\begin{bmatrix} 0&1\\ 0&0 \end{bmatrix}+ c\begin{bmatrix} 0&0\\ 1&0 \end{bmatrix}+ d\begin{bmatrix} 0&0\\ 0&1 \end{bmatrix}## Thus ##dim(V)=4##, right?

Homework Statement Let ##T:M_2 \to M_2## a linear transformation defined by ##T \begin{bmatrix} a&b\\ c&d \end{bmatrix} = \begin{bmatrix} a&0\\ 0&d \end{bmatrix}## Describe ##ker(T)## and ##range(T)##, and find their basis. Homework Equations For a linear transformation ##T:V\to W##...

Thanks for the advise. I didn't know how to use LaTeX (how do you pronounce it? though). I get to the part where I have 6 variables to express, however I'm still uncertain on how do I go into finding this variables if I only have two ##T(\vec{a}) = \vec{b}## to work with, I'm pretty sure this...

Homework Statement Let T: ℝ² → P² a linear transformation with usual operations such as T [1 1] = 1 - 2x and T [3 -1]= x+2x² Find T [-7 9] and T [a b] **Though I'm writing them here as 1x 2 row vectors , all T's are actually 2x1 column vectors (I didn't see a way to give them proper...

It is correct, both destination and domain have the usual operations.

Indeed T(0) will not map it to P² zero, it will suffice to prove the answer key is wrong. Thank you.

The good news for me is that I´ll be out on vacations from college on this date, the bad news, I don´t think I can afford a trip to the US, being a broken college student in Mexico City does not allow much of my budget for traveling (shame, shame). Still here will be visible as a partial...

Homework Statement Let be T : ℙ2 → ℙ2 a polynomial transformation (degree 2) Defined as T(a+bx+cx²) = (a+1) + (b+1)x + (b+1)x² It is a linear transformation? Homework Equations A transformation is linear if T(p1 + p2) = T(p1) + T(p2) And T(cp1)= cT(p1) for any scalar c The Attempt at...

Thank you, I didn't notice that indeed the 3rd vector is the sum of the first two, that is proof enough the key is indeed wrong.

Homework Statement Let { u, v, w} be a set of vectors linearly independent on a vector space V - Is { u-v, v-w, u-w} linearly dependent or independent? Homework Equations [/B] A set of vectors u, v, w are linearly independent if for the equation au + bv + cw= 0 (where a, b, c are real...