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beketsoBest ResponseYou've already chosen the best response.1
write the matrix\[E= \left[\begin{matrix}3 & 1 \\ 1 & 1\end{matrix}\right]\]
 one year ago

beketsoBest ResponseYou've already chosen the best response.1
as a linear combination of the matrices \[A=\left[\begin{matrix}1 & 1 \\ 1& 0\end{matrix}\right]\]
 one year ago

beketsoBest ResponseYou've already chosen the best response.1
\[B=\left[\begin{matrix}0 & 0 \\ 1 & 1\end{matrix}\right]\]
 one year ago

beketsoBest ResponseYou've already chosen the best response.1
\[C=\left[\begin{matrix}0 & 2 \\ 0 & 1\end{matrix}\right]\]
 one year ago

beketsoBest ResponseYou've already chosen the best response.1
basically ,you write the matrix E as a linear combination of the matrices A,B, and C
 one year ago

beketsoBest ResponseYou've already chosen the best response.1
@richyw ,yes there only three
 one year ago

richywBest ResponseYou've already chosen the best response.1
ok so the concepts you need here are matrix addition and scalar multiplication.
 one year ago

richywBest ResponseYou've already chosen the best response.1
you can solve this one in different ways but it's simple enough to do by inspection
 one year ago

richywBest ResponseYou've already chosen the best response.1
so looking at E, the first thing I notice is that \(e_{11}=3\) now looking at matrices A, B, and C. The only one that has anything but 0 in that position is matrix A, so we know already that it must be 3 times matrix A. which gives. \[\left[\begin{matrix}3 & 3 \\ 3 & 0\end{matrix}\right]\] right?
 one year ago

richywBest ResponseYou've already chosen the best response.1
alright so now look at matrix E and notice that position \(e_{12}\) is 2, so we need to subtract a certain amount from matrix A to produce a 2 there.
 one year ago

richywBest ResponseYou've already chosen the best response.1
well, matrix B has a zero in that position, so it is no good, so subtract one times matrix C from matrix A and we get \[3AC=\left[\begin{matrix}3&1\\3&1\end{matrix}\right]\]
 one year ago

richywBest ResponseYou've already chosen the best response.1
sorry I should have said "subtract one times matrix C from three times matrix A". Now I hope you can see what multiple of matrix B you bust subtract to get E
 one year ago

richywBest ResponseYou've already chosen the best response.1
alright cool well then you have the answer!
 one year ago
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