D. Wellington Posted October 3, 2012 Share Posted October 3, 2012 (edited) We had our first test and I'm trying to understand what it is I'm missing. I list each of the questions below, followed by what I answered. 1. Let v1=[ 1 ] and v2 = [ 1 ] --- Find a nonzero vector w that exists in R^3 such that {v1, v2, w} is linearly independent. [ 1 ] [ 2 ] [ 1 ] [ 3 ] ans: w = [ 1 ] this was assuming that as long as the vector was a multiple of the of the vectors then the set would be linearly independent. [ 4 ] [ 6 ] 2. Find the general solution to the equation A*x = 0 (where x is a vector). Give your answer in parametric vector form. A = [ 1 2 0 -2 0 ] [ 0 0 1 2 0 ] [ 0 0 0 0 1 ] ans: this one I had no idea Edited October 3, 2012 by D. Wellington Link to comment Share on other sites More sharing options...

Crimson Sunbird Posted February 11, 2013 Share Posted February 11, 2013 2. Find the general solution to the equation A*x = 0 (where x is a vector). Give your answer in parametric vector form. A = [ 1 2 0 -2 0 ] [ 0 0 1 2 0 ] [ 0 0 0 0 1 ] ans: this one I had no idea [latex]\begin{pmatrix}1 & 2 & 0 & -2 & 0 \\ 0 & 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 0 & 1\end{pmatrix}\begin{pmatrix}a \\ b \\ c \\ d \\ e\end{pmatrix}=\begin{pmatrix}a+2b-2d \\ c+2d \\ e\end{pmatrix}=\begin{pmatrix}0 \\ 0 \\ 0\end{pmatrix}[/latex] So, letting [latex]b=t,d=u[/latex], the general solution is [latex]\mathbf{x}\,=\,\begin{pmatrix}-2t+2u \\ t \\ -2u \\ u \\ 0\end{pmatrix}[/latex] Link to comment Share on other sites More sharing options...

shah_nosrat Posted May 17, 2013 Share Posted May 17, 2013 (edited) We had our first test and I'm trying to understand what it is I'm missing. I list each of the questions below, followed by what I answered. 1. Let v1=[ 1 ] and v2 = [ 1 ] --- Find a nonzero vector w that exists in R^3 such that {v1, v2, w} is linearly independent. [ 1 ] [ 2 ] [ 1 ] [ 3 ] ans: w = [ 1 ] this was assuming that as long as the vector was a multiple of the of the vectors then the set would be linearly independent. [ 4 ] [ 6 ] I don't understand your vector representations. But from the definition of linear independence, it says the following, that the linear combination of the vectors; k_{1}v_{1} + k_{2}v_{2} + k_{3}w = 0, if k_{1}=k_{2}=k_{3}=0 solving this equation will give your solution. Edited May 17, 2013 by shah_nosrat Link to comment Share on other sites More sharing options...

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