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Mathematics 10 Online
OpenStudy (anonymous):

Need help to find determinant of a matrix

OpenStudy (anonymous):

\[\left[\begin{matrix}1 & 8&\pi&.2&1&e \\ 0 &1&74&81&2&\sqrt{2}\\0&0&1&3&3&7\\0&0&0&1&4&9\\0&0&0&0&1&10^{-10}\\0&0&0&0&0&1\end{matrix}\right]\] Use the fact that \[\det A = \det A ^{T}\]

OpenStudy (anonymous):

The Matrix is A

hartnn (hartnn):

determinant of upper or lower triangular matrix is just product of diagonal elements. is this true ?

OpenStudy (anonymous):

Yes. I am confused because the most ive done is 3X3

hartnn (hartnn):

whatever be the order ... det of upper/lower triag matrix is just product of diagonal elements so gere its just 1*1*1*1 = ...

OpenStudy (anonymous):

1

hartnn (hartnn):

thats it!

OpenStudy (anonymous):

still not understanding. mind doing part of this matrix

OpenStudy (ybarrap):

As @hartnn says, since this is an upper triangular matrix, the determinant is just the product of the diagonals. Same thing for lower triangular matrices. This is the easiest type to evaluate, and since the diagonals are all 1's the answer is just 1. That's it!! Answer is 1.

hartnn (hartnn):

i am not understanding what you are not understanding lol :P

OpenStudy (anonymous):

thx i understand what i wasnt understanding lol

hartnn (hartnn):

lol ok, good :)

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