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Matrix Multipication

  • Thread starter roam
  • Start date
  • #1
1,266
11

Homework Statement



I look at the following:

[tex](x_1\,\,x_2)\begin{pmatrix}1&2\\2&4\end{pmatrix}\binom {x_1}{x_2}=(x_1\,\,x_2)\binom {x_1+2x_2}{2x_1+4x_2}=x_1^2+2x_1x_2+2x_1x_2+4x_2^2[/tex]

And I don't understand how they got from [tex](x_1\,\,x_2)\binom {x_1+2x_2}{2x_1+4x_2}[/tex] to [tex]x_1^2+2x_1x_2+2x_1x_2+4x_2^2[/tex].


The Attempt at a Solution



What process is used here? It surely is not matrix multiplication, otherwise the result would have to be a 1x2 matrix. :confused:
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Hi roam! :smile:

No, that longy thingy is a 1x2 column. :wink:
 
  • #3
93
0
Concerning matrix multiplication, the rule is that a (mxn) matrix multiplied by a (nxp) matrix gives a (mxp) matrix.
Here, you have a (1x2) matrix multiplied by a (2x2) multiplied by a (2x1). Which indeed leeds to a (1x1) matrix i.e. a number.
The part you don't understand is a (1x2) x (2x1) and applying the rules of matrix multiplication you indeed find the result :smile:
 

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