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beketso
 2 years ago
linear combinations on vectors.help
beketso
 2 years ago
linear combinations on vectors.help

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beketso
 2 years ago
Best ResponseYou've already chosen the best response.1write the matrix\[E= \left[\begin{matrix}3 & 1 \\ 1 & 1\end{matrix}\right]\]

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

beketso
 2 years ago
Best ResponseYou've already chosen the best response.1\[B=\left[\begin{matrix}0 & 0 \\ 1 & 1\end{matrix}\right]\]

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

beketso
 2 years ago
Best ResponseYou've already chosen the best response.1basically ,you write the matrix E as a linear combination of the matrices A,B, and C

beketso
 2 years ago
Best ResponseYou've already chosen the best response.1@richyw ,yes there only three

richyw
 2 years ago
Best ResponseYou've already chosen the best response.1ok so the concepts you need here are matrix addition and scalar multiplication.

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

richyw
 2 years ago
Best ResponseYou've already chosen the best response.1so 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?

richyw
 2 years ago
Best ResponseYou've already chosen the best response.1alright 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.

richyw
 2 years ago
Best ResponseYou've already chosen the best response.1well, 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 \[3AC=\left[\begin{matrix}3&1\\3&1\end{matrix}\right]\]

richyw
 2 years ago
Best ResponseYou've already chosen the best response.1sorry 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

richyw
 2 years ago
Best ResponseYou've already chosen the best response.1alright cool well then you have the answer!
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