4pie0
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3 answers
3 votes
94 views
Sum of $\sum_{n=0}^\infty \frac{(x+2)^{n+2}}{3^n} $
3 votes

for $|(x+2)/3|<1$ it converges to the limit given by multiplication of geometric series limit and polynomial: $$ \sum_{n=0}^\infty\frac{(x+2)^{n+2}}{3^n}=(x+2)^2\sum_{n=0}^\infty\left(\frac{x+2}{3}...

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1 answers
2 votes
104 views
is this solution of $AX=0$ in space VA?
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3 votes

ok, it is! we are in $mod 11$ and $X4=\begin{bmatrix}0 \\ 2 \\ 1 \\ 1\end{bmatrix}=2\begin{bmatrix}9 \\ 1 \\ 0 \\ 0\end{bmatrix}+1\begin{bmatrix}8 \\ 0 \\ 1 \\ 0\end{bmatrix}+1\begin{bmatrix}7 \\ 0 \\ ...

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2 answers
0 votes
1k views
Finding two unknown vectors
2 votes

For each $k\in \Re $ that you substitute to the final system of 3 equations you will obtain unique solution $v_{2}=(d,e,f)$ and $v_{1} = ku = (-4k,3k,-4k)$

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2 answers
1 votes
53 views
Linear Independence in R^n
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1 votes

To test the independence of vectors $v_1, v_2, ..., v_n$ you have to determine if there exists nontrivial (not all zero) solution of equation $\alpha_1 v_1 + \alpha_2v_2 + ... + \alpha_nv_n = 0$ (...

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6 answers
0 votes
116 views
Why is one of the conditions of a vector space that if I add two vectors, the sum must be within the space?
1 votes

The sum and multiplication of two vectors $u,v$ from a linear space $V$ has to belong to $V$ because we want to consider elements that share some common properties, in particular they all can be ...

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2 answers
1 votes
142 views
Simple explanation for number of solutions of system of linear equations
1 votes

0: For simplicity let's assume 2x2 matrix. Assume that after multiplication you get system of equations: $x_1 + x_2 = 5$ $x_1 + x_2 = 10$ infinity: Assume that after multiplication you get ...

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2 answers
1 votes
73 views
how to calculate partial derivative?
Accepted answer
1 votes

here it is: $$ \frac{\partial q}{\partial k}= 1p(k,l) + k \times\frac{\partial p}{\partial k}\\ \frac{\partial q}{\partial l}= k \times\frac{\partial p}{\partial l}\ \ \\\frac{\partial q}{\partial m} =...

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1 answers
1 votes
25 views
generating a vector given other vectors in modulo 11
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1 votes

$X4=\begin{bmatrix}0 \\ 2 \\ 1 \\ 1\end{bmatrix}=2\begin{bmatrix}9 \\ 1 \\ 0 \\ 0\end{bmatrix}+1\begin{bmatrix}8 \\ 0 \\ 1 \\ 0\end{bmatrix}+1\begin{bmatrix}7 \\ 0 \\ 0 \\ 1\end{bmatrix}$ $(\text{mod }...

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2 answers
2 votes
119 views
Proof of limit by definition
1 votes

for every x in [0,1] there exists n that $x> \frac{1}{n}$ so $\lim(h_n)(x)=\lim_n_{\infty}\frac{n}{n-1}(1-x)=1-x$ since x is constant for x=1 and x=0 lim=0

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1 answers
1 votes
134 views
Finding partial derivatives of a 3 variable function
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1 votes

$$ \frac{\partial q}{\partial k}= 1p(k,l) + k \times\frac{\partial p}{\partial k}\\ \frac{\partial q}{\partial l}= k \times\frac{\partial p}{\partial l}\ \ \\\frac{\partial q}{\partial m} = \frac{\...

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2 answers
3 votes
802 views
Is there a straightforward way to determine if this set is convex?
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1 votes

yes, so if this is empty, this is convex by definition. if this was meant to be sum of two sets then my solution is take one point that belongs to set of function solutions and one from other set, we ...

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2 answers
1 votes
10k views
Find a vector that spans the given set
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0 votes

I think the correct answer is $v=[-2,5,3]$ so then $Span{(v)}=Span{([-2,5,3])}=H$. Because $v\subset \mathbb{R}^3$ so $H$ is a subspace of $\mathbb{R}^3$.

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2 answers
3 votes
310 views
Finding a basis for two subspaces of $\mathbb {R}^4$
0 votes

Space $U$ is comprised of all vectors of the form $$(x_1,x_2,-x_2,\frac14x_1)$$ thus every vectorin $U$ is generated by two basis vectors: $$(x_1,x_2,-x_2,\frac14x_1) = x_1(1,0,0,\frac14)+x_2(0,1,-...

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2 answers
1 votes
2k views
Prove that if $f'(x)\gt 0$ , then the function is increasing, and if $f'(x)\lt 0 $ then the function is decreasing.
0 votes

The fact that derivative exists means that for every $h >0$ there exists (we can choose it) $\varepsilon= x-x_0>0$ such that quotient $$q=\frac{f(x_0+\varepsilon)-f(x_0)}{\varepsilon}$$ will ...

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3 answers
1 votes
411 views
Orthogonal vectors and linear systems
0 votes

If c is a scalar then $ca^T=(ca_1, ca_2,\ldots, ca_n)^T $ and unless $a_1 = a_2 = ... = a_n \not = 0 $ $ca^T\ne 1. $

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1 answers
-1 votes
57 views
Formula issues when working out chances of getting certain marks
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0 votes

you have to add ranges of individual probablillities (you can also use cumulated distribution as $P(x>=X)=1-P(x<X)=1-F(X)$ ). I think from the picture below you will get the right idea.

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4 answers
2 votes
75 views
Differentiation help required!
0 votes

treat $(f_1f_2f_3)'$ like $[(f_1f_2)f_3]'$ so from this this is obvious now: $[(f_1f_2)f_3]'=(f_1f_2)'f_3+(f_1f_2)f_3'$

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