1. ## Matrix

$\displaystyle A=\begin{vmatrix} 1 & 0&0 \\ 3& \omega &0\\ 0&3-i&\omega^2 \end{vmatrix}\\$

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

Find

1) $\displaystyle A^{105}$

2) $\displaystyle A^{106}$

3) $\displaystyle A^{108}$

4) $\displaystyle A^{109}$

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

then ..find

1) $\displaystyle A^{105}$
2) $\displaystyle A^{106}$
3) $\displaystyle A^{108}$
4) $\displaystyle A^{109}$
You need to diagonalise A to find these higher powers of A

3. 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

4. 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.

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

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

Find

1) $\displaystyle A^{105}$

2) $\displaystyle A^{106}$

3) $\displaystyle A^{108}$

4) $\displaystyle A^{109}$
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) ....

6. ya its a MATRIX

sorry its looking lik a determinant in fig

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