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Question: For which real constants a and b does the vectors [(1,a,0),(a,1,1),(b,1,1)] lie in the same plane?
So know that the lines are in the same plane when the determinant is 0 so I've calulated it like this: \[A=\left[\begin{matrix}1 & a & 0 \\ a & 1 & 1 \\b &1&1 \end{matrix}\right]\]
\[\det(A)=1\left[\begin{matrix}1 & 1 \\ 1 & 1\end{matrix}\right]a \left[\begin{matrix}a & 1\\ b & 1\end{matrix}\right]+0= a(a+b)=a( ab)\]
\[a(ab)=0 \]
\[a=0, b=a\]
It's right but the student solution guide solve it \[\left[\begin{matrix}1 & a & b \\ a & 1&1 \\ 0&1&1\end{matrix}\right]\]
 one year ago
 one year ago
Question: For which real constants a and b does the vectors [(1,a,0),(a,1,1),(b,1,1)] lie in the same plane? So know that the lines are in the same plane when the determinant is 0 so I've calulated it like this: \[A=\left[\begin{matrix}1 & a & 0 \\ a & 1 & 1 \\b &1&1 \end{matrix}\right]\] \[\det(A)=1\left[\begin{matrix}1 & 1 \\ 1 & 1\end{matrix}\right]a \left[\begin{matrix}a & 1\\ b & 1\end{matrix}\right]+0= a(a+b)=a( ab)\] \[a(ab)=0 \] \[a=0, b=a\] It's right but the student solution guide solve it \[\left[\begin{matrix}1 & a & b \\ a & 1&1 \\ 0&1&1\end{matrix}\right]\]
 one year ago
 one year ago

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frxBest ResponseYou've already chosen the best response.0
they are using that one as a determinate, is my solution equally right or should I spend some time learn there way?
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
equally right. it's a property of the determinant that transposing it will not change the value of the determinant
 one year ago
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