How do I transform a matrix from one basis to another?

[transgalactic]

i added a link with the question
and a solution

http://img518.imageshack.us/my.php?image=img8267rf4.jpg

i want to transform a matrix from a standart basis to basis B
A-out old matrix
X- the old basis
Y-the new basis
S-the transformation matrix
S^-1 -its inverse

N-resolt
i did
Y|X>>>I|S

S|I=I|S^-1

N=S*A*S^-1

in some metrices i got fractures so i multiplied by the dinominator the whole line

that what i did
i don't know where i did a mistake

or wether this method is ok

 

[HallsofIvy]

The method is ok and it looks like you did it correctly.

 

[transgalactic]

the answer is different i don't know
how he did what he did
and he got full points for this

http://img352.imageshack.us/my.php?image=45865659to7.jpg?

 

[transgalactic]

i tried many times to solve it but i can't get nor to the formal answer nor
to understand the formal solution

can some solve it from the start to the end

 

[HallsofIvy]

Sorry, I didn't look closely enough. You have, as the inverse to
S^{-1}= \left(\begin{array}{ccc} 2 & -1 & 1 \\ 1 & 2 & 0 \\ 1 & 1 & 1 \end{array}\right)
S= \left(\begin{array}{ccc} \frac{1}{2} & \frac{1}{2} & -\frac{1}{2} \\ -\frac{1}{4} & \frac{1}{4} & \frac{1}{4} \\ -\frac{1}{4} & -\frac{3}{4} & \frac{5}{4} \end{array}\right)
That is correct.

However, in "S*A*S^-1" you have removed the denominators! Why did you do that? I know you said "i got fractures so i multiplied by the dinominator the whole line" but that, of course, changes the matrix. You will need to go back and divide each line by that multiplier.

 

[transgalactic]

i can't get to the answer of the solution that i was given

i am not sure about how to build the S matrix

(of transformation from one basis to the other)

 

[HallsofIvy]

I told you that the S matrix is exactly what you said:
S= \left(\begin{array}{ccc} \frac{1}{2} & \frac{1}{2} & -\frac{1}{2} \\ -\frac{1}{4} & \frac{1}{4} & \frac{1}{4} \\ -\frac{1}{4} & -\frac{3}{4} & \frac{5}{4} \end{array}\right)

My question was "Why didn't you use that?"

 

[transgalactic]

i did use that

as you can see in my soltuion i multiplied the first one by 2

the second one by 4
and the third one by 4
so as you you said i need to divide the resolt by these numbers

i took the resolt
and i tried to divide the rows by
1/32
but no way that whould give me the formal answer