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thomas5267
 one year ago
Two proofs needed:
1. Prove or provide a counterexample that matrices of the following form must be singular.
\[
\begin{pmatrix}
n&n+1&n+2\\
n+3&n+4&n+5\\
n+6&n+7&n+8
\end{pmatrix}
\]
2. Prove the triple product identity.
\[
\underline{a}\times (\underline{b}\times \underline{c}) = \underline{b}(\underline{a}\cdot\underline{c})  \underline{c}(\underline{a}\cdot\underline{b})
\]
thomas5267
 one year ago
Two proofs needed: 1. Prove or provide a counterexample that matrices of the following form must be singular. \[ \begin{pmatrix} n&n+1&n+2\\ n+3&n+4&n+5\\ n+6&n+7&n+8 \end{pmatrix} \] 2. Prove the triple product identity. \[ \underline{a}\times (\underline{b}\times \underline{c}) = \underline{b}(\underline{a}\cdot\underline{c})  \underline{c}(\underline{a}\cdot\underline{b}) \]

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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2for first question try below : R2  R1 R3  R1

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.1It is very unfortunate that the lecutrer try to use the vectors \[ \underline{a}=\begin{pmatrix}1&2&3\end{pmatrix}^T\\ \underline{b}=\begin{pmatrix}4&5&6\end{pmatrix}^T\\ \underline{c}=\begin{pmatrix}7&8&9\end{pmatrix}^T \] to demonstrate the scalar triple product. He wanted to demonstrate that the scalar triple product corresponded to the volume of the parallelepiped of formed by that three vectors. As \[ \underline{a}\cdot(\underline{b}\times\underline{c})= \begin{vmatrix} 1&2&3\\ 4&5&6\\ 7&8&9 \end{vmatrix} \] and matrix of the form \[ \begin{pmatrix} n&n+1&n+2\\ n+3&n+4&n+5\\ n+6&n+7&n+8 \end{pmatrix} \] are always singular, you can see how this goes!

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.1Proven by standard Gaussian elimination. I was expecting some ingenious prove without using it.
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