1. Change of basis matrix

Find the change-of-basis matrix from B to C

B = $\displaystyle \begin{bmatrix}-1&-2&0\\1&3&2\\2&1&-7 \end{bmatrix}$

C = $\displaystyle \begin{bmatrix}1&-2&-1\\-1&1&-2\\0&-1&-2 \end{bmatrix}$

Change-of-basis = $\displaystyle C^{-1} * B$

change-of-basis from B to C = $\displaystyle \begin{bmatrix}-9&36&59\\4&-17&-29\\-2&8&13 \end{bmatrix}$

Does this seem right? I am a little unsure because it says from B to C so i wasnt sure if i should use the inverse of C or the inverse of B in my change-of-basis formula i listed above.

Thank you

p.s. if it would have been find the change-of-basis matrix from C to B would the formula i use be $\displaystyle B^{-1} * C$?

Thanks for any help

2. Originally Posted by mybrohshi5
Find the change-of-basis matrix from B to C

B = $\displaystyle \begin{bmatrix}-1&-2&0\\1&3&2\\2&1&-7 \end{bmatrix}$

C = $\displaystyle \begin{bmatrix}1&-2&-1\\-1&1&-2\\0&-1&-2 \end{bmatrix}$

Change-of-basis = $\displaystyle C^{-1} * B$

change-of-basis from B to C = $\displaystyle \begin{bmatrix}-9&36&59\\4&-17&-29\\-2&8&13 \end{bmatrix}$

Does this seem right? I am a little unsure because it says from B to C so i wasnt sure if i should use the inverse of C or the inverse of B in my change-of-basis formula i listed above.

Thank you

p.s. if it would have been find the change-of-basis matrix from C to B would the formula i use be $\displaystyle B^{-1} * C$?

Thanks for any help
$\displaystyle C^{-1}B=\begin{bmatrix} -11 & -4 & 41\\ -6 & -1 & 25\\ 2 & 0 & -9 \end{bmatrix}$

From C to B, you have the correct formula.