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[SOLVED] Show Matrix A is not invertible

delgeezee

New member
May 24, 2013
9
SHow that matrix A is not invertible, where
A =
\(\displaystyle cos^2 \alpha\)\(\displaystyle sin^2 \beta\)\(\displaystyle cos^2 \theta\)
aaa
\(\displaystyle sin^2 \alpha\)\(\displaystyle cos^2 \beta\)\(\displaystyle sin^2 \theta\)
 

tkhunny

Well-known member
MHB Math Helper
Jan 27, 2012
267
Have you considered the Determinant?
 

delgeezee

New member
May 24, 2013
9
Have you considered the Determinant?
Yes i know if the det = 0 then the matrix is not invertible, or if i can introduce a row or columns of zeros its not invertible.

im not sure but maybe there is something involved with transformations.
 

Petrus

Well-known member
Feb 21, 2013
739
Yes i know if the det = 0 then the matrix is not invertible, or if i can introduce a row or columns of zeros its not invertible.

im not sure but maybe there is something involved with transformations.
Hello delgeezee,
If matrice \(\displaystyle A\) is invertible Then \(\displaystyle A^T\) is Also invertible
Regards,
\(\displaystyle |\pi\rangle\)
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,779
Welcome to MHB, delgeezee! :)

Yes i know if the det = 0 then the matrix is not invertible, or if i can introduce a row or columns of zeros its not invertible.

im not sure but maybe there is something involved with transformations.
Yes. It involves transformations that are applicable to determinants.
In particular you can add or subtract a multiple of any row to another row.
The determinant will remain the same under such a transformation.
 

Petrus

Well-known member
Feb 21, 2013
739
Welcome to MHB, delgeezee! :)



Yes. It involves transformations that are applicable to determinants.
In particular you can add or subtract a multiple of any row to another row.
The determinant will remain the same under such a transformation.
Hello,
After I read I like Serena post I realised I missunderstand you did not ask about transport..
I will citate from Ackbach:
"The ERO that takes a multiple of one row, adds it to another row, and stores it in that row, does not change the determinant.

The ERO that switches two rows multiplies the determinant by $-1$.

The ERO that multiplies a row by a nonzero number $m$ also multiplies the determinant by $m$"


Regards,
\(\displaystyle |\pi\rangle\)
 

delgeezee

New member
May 24, 2013
9
Hello,
After I read I like Serena post I realised I missunderstand you did not ask about transport..
I will citate from Ackbach:
"The ERO that takes a multiple of one row, adds it to another row, and stores it in that row, does not change the determinant.

The ERO that switches two rows multiplies the determinant by $-1$.

The ERO that multiplies a row by a nonzero number $m$ also multiplies the determinant by $m$"


Regards,
\(\displaystyle |\pi\rangle\)
Thank I was able to introduce a row of zeros by reducing the determinant matrices to upper triangular form thus making the determinant = 0 by taking the cofactor expansion along the row of zeros.