Question

Let $B = \{(1, 1, 0), (0, 1, 1), (1, 0, 1)\}$ and $B' = \{(1, 0, 0), (0, 1, 0), (0, 0, 1)\}$ be bases for $\mathbb{R}^3$, and let $A = \begin{bmatrix} \frac{1}{2} & \frac{-1}{2} & \frac{5}{2} \\ 2 & 1 & 2 \\ \frac{-1}{2} & \frac{3}{2} & \frac{1}{2} \end{bmatrix}$ be the matrix for $T: \mathbb{R}^3 \to \mathbb{R}^3$ relative to $B$. (a) Find the transition matrix $P$ from $B'$ to $B$. (b) Use the matrices $P$ and $A$ to find $[v]_B$ and $[T(v)]_B$, where $[v]_{B'} = \begin{bmatrix} 0 \\ -1 \\ 1 \end{bmatrix}$.

Name: let b 1 1 0 0 1 1 1 0 1 and b 1 0 0 0 1 0 0 0 1 be bases for mathbbr3 and let a beginbmatrix frac12 frac 12 frac52 2 1 2 frac 12 frac32 frac12 endbmatrix be the matrix for t mathbbr3 to math 22112
Uploaded: 2023-08-30T17:57:18-08:00
Duration: 2 min 54 s
Channel: Adi S
Description: let b 1 1 0 0 1 1 1 0 1 and b 1 0 0 0 1 0 0 0 1 be bases for mathbbr3 and let a beginbmatrix frac12 frac 12 frac52 2 1 2 frac 12 frac32 frac12 endbmatrix be the matrix for t mathbbr3 to math 22112

          Let $B = \{(1, 1, 0), (0, 1, 1), (1, 0, 1)\}$ and $B' = \{(1, 0, 0), (0, 1, 0), (0, 0, 1)\}$ be bases for $\mathbb{R}^3$, and let
$A = \begin{bmatrix} \frac{1}{2} & \frac{-1}{2} & \frac{5}{2} \\ 2 & 1 & 2 \\ \frac{-1}{2} & \frac{3}{2} & \frac{1}{2} \end{bmatrix}$
be the matrix for $T: \mathbb{R}^3 \to \mathbb{R}^3$ relative to $B$.
(a) Find the transition matrix $P$ from $B'$ to $B$.
(b) Use the matrices $P$ and $A$ to find $[v]_B$ and $[T(v)]_B$, where
$[v]_{B'} = \begin{bmatrix} 0 \\ -1 \\ 1 \end{bmatrix}$.

$let b 1 1 0 0 1 1 1 0 1 and b 1 0 0 0 1 0 0 0 1 be bases for mathbbr3 and let a beginbmatrix frac12 frac 12 frac52 2 1 2 frac 12 frac32 frac12 endbmatrix be the matrix for t mathbbr3 to math 22112$

Added by Terry G.

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