matrix, find the determinent

[raven2k7]

can anyone explain to me how to resolve this (using the cramers method if possible). the file is attached

 

[Deleted member 4993]

can anyone explain to me how to resolve this (using the cramers method if possible). the file is attached

To solve this problem, you do NOT use Cramer's Rule. Cramers rule is used to solve a set of linear equation. Here you have to use some of the properties of determinants that you have used before (e.g. row or column addition does not change the value of the determinant). Make list of those properties - and you have to use those several times.

For example, I'll start working with matrix a) and "switch" columns {2} and {3} - so that it starts to look like the given matrix in the problem. This operation will leave the determinant unchanged.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[HallsofIvy]

Do you know some basic "algebraic" rules for determinants? For example, if you know that \(\displaystyle \left|\begin{array}{ccc}a & b & 5c \\ d & e & 5f \\ g & h & 5i\end{array}\right|=5\left|\begin{array}{ccc}a & b & c \\ d & e & f \\ g & h & i\end{array}\right|\) that makes it a little simpler!

 

[raven2k7]

oh wow , thats why i was stuck , didnt know i had to change the rows around , thats interesting , ok ill give it a try then show u what i got

Do you know some basic "algebraic" rules for determinants? For example, if you know that \(\displaystyle \left|\begin{array}{ccc}a & b & 5c \\ d & e & 5f \\ g & h & 5i\end{array}\right|=5\left|\begin{array}{ccc}a & b & c \\ d & e & f \\ g & h & i\end{array}\right|\) that makes it a little simpler!

oh, what you are saying is if a constant is multiplied by a row or column then its also the determinent?