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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 dont 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]= [d_{1}d_{2}d_{3}...d_{m}]^{T}

W[tex]\in[/tex]R^{n}

[tex]\vec{x}[/tex]_{i}=[x_{i1}x_{i2}... x_{in}]^{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

2. Relevant equations

3. 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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# Homework Help: Help with Linear Algebra exercise!

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