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}##...
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...
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...
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...