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2d
comment Finding a matrix with respect to a basis
My solution presumed the basis was changed in both the domain and range, the solution in the link only changes the domain basis.
2d
comment Rate of change of a function
The real question is, are they grass fed?
2d
comment Prove $\lim\limits_{n \to \infty} \frac{n^2+1}{5n^2+n+1}=\frac{1}{5}$ directly from the definition of limit.
You can replace the denominator by $25 n^2$.
2d
comment Use the Intermediate Value Theorem to show the equation
The intermediate value theorem shows that a solution exists in $(-{\pi \over 2}, {\pi \over 2})$ and periodicity shows the rest.
2d
comment Finding a matrix with respect to a basis
If the basis is only changed for the domain then this is correct. I presumed the basis was changed in both the domain and range.
Apr
16
comment How do I find this basis given matrix representations?
You can solve the system $\phi(B) = 0$ above, this is underdetermined, since $\dim \ker \phi = 2$. You just need to ensure that any solution is invertible.
Apr
16
comment Derivation: Discerning difference between arithmetic expression with parenthesis versus without using abstract syntax trees
Then there is no ambiguity.
Apr
16
comment Derivation: Discerning difference between arithmetic expression with parenthesis versus without using abstract syntax trees
You can write $a+b+c$ as $a+(b+c)$ or $(a+b)+c$, for example (unless you have some presumed associativity).
Apr
16
comment Derivation: Discerning difference between arithmetic expression with parenthesis versus without using abstract syntax trees
That is not what I was thinking. I was thinking of something like $(+\ (*\ 3\ 4)\ (+\ \ (* \ 5 \ 6) \ 7))$ as an alternative to that in my first comment.
Apr
16
comment Derivation: Discerning difference between arithmetic expression with parenthesis versus without using abstract syntax trees
No critique, just pointing out that neither tree is unique. The addition (or multiplication) is binary and can be grouped in two ways, the usual convention is left associative.
Apr
16
comment Derivation: Discerning difference between arithmetic expression with parenthesis versus without using abstract syntax trees
The tree is not unique. Here is one: $(+\ (+\ (*\ 3\ 4)\ (* \ 5 \ 6)) \ 7)$.
Apr
16
comment Showing linear independence of $\{5, e^{ax}, e^{bx}\}$
I assume that $a \neq b$ and both are non-zero? In that case suppose they are linearly dependent and show a contradiction.
Apr
14
comment Prove Product Property of Eigen Vectors
Just compute $ABu$ for Justin's sake.
Apr
14
comment For subspaces $S,U,W$ of a $K$-vector space, prove $S\cap\langle U\cup W\rangle=\langle\langle S\cap U\rangle\cup\langle S\cap W\rangle\rangle$
What are you asking?
Apr
14
comment About random variable X, which is a certain number of cars that can pass over a bridge in a 5 minute period
I have no idea what you are asking.
Apr
14
comment derivative of a linear mapping
Why the downvote?
Apr
14
comment Is it possible to write an Unambiguous Grammar for Two Hard Language ?!?
And you are required to prove that the grammar is unambiguous?
Apr
14
comment Is it possible to write an Unambiguous Grammar for Two Hard Language ?!?
I am curious to know for what sort of job it is useful to be able to create unambiguous grammars for a cooked up language?
Apr
14
comment Is it possible to write an Unambiguous Grammar for Two Hard Language ?!?
I am curious, was this for a specific job or just a generic test of some sort?
Apr
14
comment How to apply Cauchy-Schwarz inequality to show an infinite series is bounded?
Let $x_t = \delta^tr(s_t,a_t)$, then $|S_n-S_m| = |x_n+x_{n-1}+\cdots + x_{m+1}| \le |x_n|+\cdots+|x_{m+1}|$.