anonymous
  • anonymous
linear combinations on vectors.help
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
write the matrix\[E= \left[\begin{matrix}3 & 1 \\ 1 & -1\end{matrix}\right]\]
anonymous
  • anonymous
as a linear combination of the matrices \[A=\left[\begin{matrix}1 & 1 \\ 1& 0\end{matrix}\right]\]
anonymous
  • anonymous
\[B=\left[\begin{matrix}0 & 0 \\ 1 & 1\end{matrix}\right]\]

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anonymous
  • anonymous
\[C=\left[\begin{matrix}0 & 2 \\ 0 & -1\end{matrix}\right]\]
richyw
  • richyw
are there just three?
anonymous
  • anonymous
basically ,you write the matrix E as a linear combination of the matrices A,B, and C
anonymous
  • anonymous
@richyw ,yes there only three
richyw
  • richyw
ok so the concepts you need here are matrix addition and scalar multiplication.
richyw
  • richyw
you can solve this one in different ways but it's simple enough to do by inspection
richyw
  • richyw
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?
anonymous
  • anonymous
ok i got that part
richyw
  • richyw
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.
richyw
  • richyw
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 \[3A-C=\left[\begin{matrix}3&1\\3&1\end{matrix}\right]\]
richyw
  • richyw
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
richyw
  • richyw
are you following?
anonymous
  • anonymous
yeah
richyw
  • richyw
alright cool well then you have the answer!
anonymous
  • anonymous
so it is 3A-2B-C=E?
richyw
  • richyw
yes!
anonymous
  • anonymous
thanx a lot!!!!!!!

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