# Determinants of A and B

• Apr 5th 2008, 01:07 PM
al1850
Determinants of A and B
Find the Determinants of A and B.
Please show me how to do it,especially for B.
• Apr 5th 2008, 01:21 PM
Mathstud28
To show you
using latex would take forever...so I suggest you look up either the "alternate method" or "expansion by cofactors" method of finding determinants...I generally prefer the alternate method for 3X3 matricies for their simplicity...but to make sure you understand..the answer for B is 1
• Apr 5th 2008, 01:22 PM
galactus
You can find the det, this way:

$\begin{bmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22} &a_{23}\\a_{31}&a_{32}&a_{33}\end{bmatrix}$

$det=a_{11}a_{22}a_{33}+a_{12}a_{23}a_{31}+a_{13}a_ {21}a_{32}-a_{13}a_{22}a_{31}-a_{12}a_{21}a_{33}-a_{11}a_{23}a_{32}$

I will use x instead of theta for less typing:

$(cosx)(cosx)(1)+sinx(0)(0)+(0)(-sinx)(0)-(0)(cosx)(0)$ $-(sinx)(-sinx)(1)-(cosx)(0)(0)=cos^{2}x+sin^{2}x=1$
• Apr 5th 2008, 01:29 PM
Moo
Hello,

If you have a matrix :

$\begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}$

Write :

$\begin{pmatrix} a & b & c & a & b \\ d & e & f & d & e \\ g & h & i & g & h \end{pmatrix}$

The determinant will be found by adding the product of terms in the diagonals from up-left to down-right and substracting the product of terms in the diagonals from up-right to down-left.

$\begin{pmatrix} \boxed{a} & \boxed{b} & \boxed{c} & a & b \\ d & \boxed{e} & \boxed{f} & \boxed{d} & e \\ g & h & \boxed{i} & \boxed{g} & \boxed{h} \end{pmatrix}$

aei+bfg+cdh

$\begin{pmatrix} a & b & \boxed{c} & \boxed{a} & \boxed{b} \\ d & \boxed{e} & \boxed{f} & \boxed{d} & e \\ \boxed{g} & \boxed{h} & \boxed{i} & g & h \end{pmatrix}$

-ceg-afh-bdi

The determinant is : aei+bfg+cdh-ceg-afh-bdi
• Apr 5th 2008, 04:09 PM
al1850
thanks,you guys are always so helpful, no matter how small or simple my questions are ;-)