Math Solutions

[Step-by-Step] Let S=

Question: Let

\[S=\left\{ \left[ \begin{matrix} 1 \\ 2 \\ \end{matrix} \right],\left[ \begin{matrix} 0 \\ 1 \\ \end{matrix} \right] \right\},\,\,\,\,T=\left\{ \left[ \begin{matrix} 1 \\ 1 \\ \end{matrix} \right],\left[ \begin{matrix} 2 \\ 3 \\ \end{matrix} \right] \right\}\]

be ordered bases for \({{R}^{2}}\). Let

\[v=\left[ \begin{matrix} 1 \\ 5 \\ \end{matrix} \right],\,\,\,w=\left[ \begin{matrix} 5 \\ 4 \\ \end{matrix} \right]\]
  1. Find the coordinate vectors of v and w with respect to the basis T .
  2. What is the transition matrix \({{P}_{S\leftarrow T}}\) from the T -basis to the S-basis?
  3. Find the coordinate vectors of v and w with respect to S using \({{P}_{S\leftarrow T}}\)
  4. Find the coordinate vector of v and w with respect to S directly
  5. Find the transition matrix \({{Q}_{T\leftarrow S}}\) from the S -basis to the T -basis?
  6. Find the coordinate vectors of v and w with respect to T using \({{Q}_{T\leftarrow S}}\).

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Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document


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