## KonradZuse 3 years ago 4.10 #1. In Exercise 1 let T[a] and T[b] be the operators whose standard matrices are given. Find the standard matrices for T[a] o T[b] and T[b] o T[a]

A =$\left[\begin{matrix}1 & -2 & 0 \\ 4 & 1 & -3 \\ 5 & 2 & 4\end{matrix}\right]$ B = $\left[\begin{matrix}2 & -3 & 3 \\ 5 & 0 & 1 \\ 6 & 1 & 7\end{matrix}\right]$ @satellite73

2. UnkleRhaukus

what do you mean by the little circle o

it's just what the book says, let me screen shot.

4. UnkleRhaukus

what does it mean

I believe it says the composite of linear transformations.

http://tutorial.math.lamar.edu/Classes/LinAlg/LinearTransformations.aspx This has it at the bottom as well, it's not really explaining how we get to an answer... I see from the previous section 4.9 that we use rotations and such but.....

Save me :).

It gives me the answer already, but I want to know why that's the answer and how to get it...

10. UnkleRhaukus

so $T_A \circ T_b = T_A ( T_b(x) )$

mhm

but there is no x here?

nor does it say what kind of transformation we are performing...?

14. UnkleRhaukus

try this $T_A\circ T_B=\text A\text B=\left[\begin{matrix}1 & -2 & 0 \\ 4 & 1 & -3 \\ 5 & 2 & 4\end{matrix}\right]\left[\begin{matrix}2 & -3 & 3 \\ 5 & 0 & 1 \\ 6 & 1 & 7\end{matrix}\right]=$

$\left[\begin{matrix}-8 & -3 & 1 \\ -5 & -15 & -8 \\ 44 & -11 & 45\end{matrix}\right]$

wow... Is that all we needed to do? That's some BS LOL.....

17. UnkleRhaukus

looks good