- #1
vslo
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Homework Statement
Hi guys,
I am new to this forum. I got a final exam tomorrow and the professor told us to solve some exercise before it. I came up with one exercise that I don't know how to do, at all.
Hope you guys can give me some light. Here it goes.
Know that the multiplication of a matrix by a vector can be write as :
[tex]\left[ \begin{array}{c} b1 \\ . \\ bn \end{array} \right]\; =\; \left[ \begin{array}{ccc} A11 & . & A1n \\ . & . & . \\ Am1 & . & Amn \end{array} \right]\; .\; \left[ \begin{array}{c} x1 \\ . \\ xn \end{array} \right][/tex]
or like [tex]bi=\sum_{j=1}^{n}{\; } \mbox{Ai}jxj\; ,\; i\; =1,2,3,...,m\; ,\; j=\; 1,2,3,\; ...,\; n[/tex]
a) prove that :
||[tex]\vec{d}[/tex] - [tex]\vec{w}[/tex] [tex]\underline{x}[/tex]||2 = [tex]\sum_{i=1}^{m}{\; }\left( d_{i}\; -x_{i}^{T}w\; \; \right)^{2}[/tex]
where [tex]\vec{d}[/tex]= [d1 d2 d3...dm]T
W[tex]\in[/tex]Rn
[tex]\vec{x}[/tex]i=[xi1 xi2 ... xin ]T
[tex]\underline{x}[/tex]= [[tex]\vec{x}[/tex]1 [tex]\vec{x}[/tex]2 ... [tex]\vec{x}[/tex]m ]
b) Prove that [tex]\underline{x}[/tex]T[tex]\underline{x}[/tex] is real and simetric.
Obs: [tex]\underline{x}[/tex] means the matrix x
Homework Equations
The Attempt at a Solution
None of my attempts were close to something
Hope you guys understand the question and give me a hand !
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