Question

change of basis

Answer 1

ugh i though i didn't need to be specific

Answer 2

\[ A \space VERY \space HUGE \space WELCOME \space IN \space OPEN \space STUDY\]
@st0rmbreaK

Answer 3

Let B = {(1, -4),(4, -15)} and S be the standard basis of R2 and {(-42, -12),(165, -47)} be a linear transform expressed in terms of the standard basis.

1. What is the change of basis matrix P_SB?
2. Find P_BS (this one I know)
3. What is the linear transform expressed in terms of the basis B?

Any help would ne appreciated followed by an explanation :D

Answer 4

thanks mayankdevnani

Answer 5

Do you get the S is the standard basis part?

Answer 6

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

Answer 7

The change of basis from A to B is found basically this way:
Augment B in front of A, so [B|A].
Now rref B to \(\mathrm{I}\) to get [\(\mathrm{I}\)|?] where ? is your transition matrix that gets you there.

A little more discusion on this:
http://www.math.uconn.edu/~judge/math2210s13/4.7.pdf