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for $|(x+2)/3|<1$ it converges to the limit given by multiplication of geometric series limit and polynomial: $$\sum_{n=0}^\infty\frac{(x+2)^{n+2}}{3^n}=(x+2)^2\sum_{n=0}^\infty\left(\frac{x+2}{3}... View answer 1 answers 2 votes 104 views Accepted answer 3 votes ok, it is! we are in mod 11 and X4=\begin{bmatrix}0 \\ 2 \\ 1 \\ 1\end{bmatrix}=2\begin{bmatrix}9 \\ 1 \\ 0 \\ 0\end{bmatrix}+1\begin{bmatrix}8 \\ 0 \\ 1 \\ 0\end{bmatrix}+1\begin{bmatrix}7 \\ 0 \\ ... View answer 2 answers 0 votes 1k views 2 votes For each k\in \Re  that you substitute to the final system of 3 equations you will obtain unique solution v_{2}=(d,e,f) and v_{1} = ku = (-4k,3k,-4k) View answer 2 answers 1 votes 53 views Accepted answer 1 votes To test the independence of vectors v_1, v_2, ..., v_n you have to determine if there exists nontrivial (not all zero) solution of equation \alpha_1 v_1 + \alpha_2v_2 + ... + \alpha_nv_n = 0 (... View answer 6 answers 0 votes 116 views 1 votes The sum and multiplication of two vectors u,v from a linear space V has to belong to V because we want to consider elements that share some common properties, in particular they all can be ... View answer 2 answers 1 votes 142 views 1 votes 0: For simplicity let's assume 2x2 matrix. Assume that after multiplication you get system of equations: x_1 + x_2 = 5 x_1 + x_2 = 10 infinity: Assume that after multiplication you get ... View answer 2 answers 1 votes 73 views Accepted answer 1 votes here it is:$$ \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} =...
$X4=\begin{bmatrix}0 \\ 2 \\ 1 \\ 1\end{bmatrix}=2\begin{bmatrix}9 \\ 1 \\ 0 \\ 0\end{bmatrix}+1\begin{bmatrix}8 \\ 0 \\ 1 \\ 0\end{bmatrix}+1\begin{bmatrix}7 \\ 0 \\ 0 \\ 1\end{bmatrix}$ $(\text{mod }... View answer 2 answers 2 votes 119 views 1 votes for every x in [0,1] there exists n that$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 View answer 1 answers 1 votes 134 views Accepted answer 1 votes $$\frac{\partial q}{\partial k}= 1p(k,l) + k \times\frac{\partial p}{\partial k}\\ \frac{\partial q}{\partial l}= k \times\frac{\partial p}{\partial l}\ \ \\\frac{\partial q}{\partial m} = \frac{\... View answer 2 answers 3 votes 802 views Accepted answer 1 votes yes, so if this is empty, this is convex by definition. if this was meant to be sum of two sets then my solution is take one point that belongs to set of function solutions and one from other set, we ... View answer 2 answers 1 votes 10k views Accepted answer 0 votes I think the correct answer is v=[-2,5,3] so then Span{(v)}=Span{([-2,5,3])}=H. Because v\subset \mathbb{R}^3 so H is a subspace of \mathbb{R}^3. View answer 2 answers 3 votes 310 views 0 votes Space U is comprised of all vectors of the form$$(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,-... View answer 2 answers 1 votes 2k views 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 ... View answer 3 answers 1 votes 411 views 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. $View answer 1 answers -1 votes 57 views Accepted answer 0 votes you have to add ranges of individual probablillities (you can also use cumulated distribution as$P(x>=X)=1-P(x<X)=1-F(X)$). I think from the picture below you will get the right idea. View answer 4 answers 2 votes 75 views 0 votes treat$(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'\$