# Matrix

• March 29th 2010, 01:19 AM
banku12
Matrix
$A=\begin{vmatrix}
1 & 0&0 \\
3& \omega &0\\
0&3-i&\omega^2
\end{vmatrix}\\$

where i is iota and w is cube root of unity.

Find

1) $A^{105}$

2) $A^{106}$

3) $A^{108}$

4) $A^{109}$
• March 29th 2010, 01:59 AM
pickslides
Quote:

Originally Posted by banku12
$A=\begin{vmatrix}
1 & 0&0 \\
3& \omega &0\\
0&3-i&\omega^2
\end{vmatrix}\\$

then ..find

1) $A^{105}$
2) $A^{106}$
3) $A^{108}$
4) $A^{109}$

You need to diagonalise A to find these higher powers of A

• March 29th 2010, 02:18 AM
banku12
Quote:

Originally Posted by pickslides
You need to diagonalise A to find these higher powers of A

ok thanks

but can u jus solve the first one for me.....it wud help me in doing rest

i will solve rest by myself....plz do the first one :)

btw it went abov my head

if suppose i need to find the trace of the higher powers do i hav to follow that method only or der is some other way also
• March 29th 2010, 02:38 AM
Bacterius
Quote:

Originally Posted by banku12
ok thanks

but can u jus solve the first one for me.....it wud help me in doing rest

i will solve rest by myself....plz do the first one :)

btw it went abov my head

if suppose i need to find the trace of the higher powers do i hav to follow that method only or der is some other way also

You really should read the text proposed by Pickslides. It will help you a lot more than just looking at a mysterious example.
• March 29th 2010, 02:46 AM
mr fantastic
Quote:

Originally Posted by banku12
$A=\begin{vmatrix}
1 & 0&0 \\
3& \omega &0\\
0&3-i&\omega^2
\end{vmatrix}\\$

where i is iota and w is cube root of unity.

Find

1) $A^{105}$

2) $A^{106}$

3) $A^{108}$

4) $A^{109}$

Is A meant to be the determinant (that's what the notation you've used means)? If so, the questions are trivial (since the matrix is lower triangular) ....
• March 29th 2010, 02:53 AM
banku12
ya its a MATRIX

sorry its looking lik a determinant in fig

Quote:

Originally Posted by Bacterius
You really should read the text proposed by Pickslides. It will help you a lot more than just looking at a mysterious example.

i din understand that stuff...thats why asking to give the soln for first