Home / Expert Answers / Other Math / 2-consider-the-following-two-bases-for-mathbb-r-2-begin-aligned-mathcal-b-pa672

(Solved): 2. Consider the following two bases for \( \mathbb{R}^{2} \) : \[ \begin{aligned} \mathcal{B} &= ...



2. Consider the following two bases for \( \mathbb{R}^{2} \) :
\[
\begin{aligned}
\mathcal{B} &=\left\{\alpha_{1}, \alpha_{2}

(a) Determine the coordinate matrix \( [\alpha]_{\mathcal{B}} \) for the vector \( \alpha=(-4,9) \).
(b) Compute the unique t

2. Consider the following two bases for \( \mathbb{R}^{2} \) : \[ \begin{aligned} \mathcal{B} &=\left\{\alpha_{1}, \alpha_{2}\right\}=\{(-7,3),(2,-1)\} \\ \mathcal{B}^{\prime} &=\left\{\alpha_{1}^{\prime}, \alpha_{2}^{\prime}\right\}=\{(5,-1),(1,6)\} . \end{aligned} \] (a) Determine the coordinate matrix \( [\alpha]_{\mathcal{B}} \) for the vector \( \alpha=(-4,9) \). (b) Compute the unique transition matrix \( P \) between \( \mathcal{B} \) and \( \mathcal{B}^{\prime} \). (c) Use the result of Part (a) to determine the coordinate matrix \( [\alpha]_{\mathcal{B}^{\prime}} \) for the vector \( \alpha=(-4,9) \).


We have an Answer from Expert

View Expert Answer

Expert Answer


We have an Answer from Expert

Buy This Answer $5

Place Order

We Provide Services Across The Globe