Sarahisme

would anyone be able to give me a hint to get me going with this problem, i am unsure as what i should start by doing... small hint? Cheers Sarah

oh ok so i think i was right then thanks matt i just wasnt sure of a formal way of saying it, "any linearly independent set iwth n elements in a n n dimensional space must be a basis" i think that must be a thm. somewhere in my book, although i cannot yet find it. but i suppose so long as i say that and include what i did above (showing that p_1, p_2 & p_3 are linearly indepedent) then it sounds complete to me

yes drjava is a little slow, but its interactions pane is very useful and yeah its nice a simple

thats ok well the fact that my name is SARAHisme you know, might just be subtle giveaway

or can i just say that well, i have shown they are linearly indepedent, and they obviously span P_2, beause there are non-zero coeffiencts for each bit (t^2, t, constant) etc. but doing this would seem extemely dodget to me :S

excuse me....

but has what i did in post #2 shown that B is a basis for P_2 ??

ok, yep, i agree with that

like how do i show that: P_2 = span{beta} = span{p_1, p_2, p_3} ???

so how do you show something is a basis then? do you just have to show that it spans P_2 and that the things in the subset are linearly independent?

yeah thats what i did, so i think i've got part (b) done, and i sort of showed what i did, with those 2 matrices there (the second one is the rref form of the other)

how do i show that the subset beta spans P_2?

wait, no, i think i do know how to do part (b): like this... and so you have p(t) = (16/27)p1(t) + (1/27)p2(t) + (7/18)p3(t) yep??

aghhhh i can't remember how to do (b), :S

i use drjava, what do people think of that? i think its a good one for beginners

ok so for part (a) to show they are linearly independent, you put them in a matrix augmented with a column of 0's (zeros) on the end: [math] \[ \left( \begin{array}{cccc} 2 & -1 & 3 & 0 \\ -5 & 1 & 0 & 0 \\ 0 & 4 & -2 & 0 \end{array} \right)\] [/math] then row reduce to reduced row echelon form so this goes to this (after a few steps) [math] \[ \left( \begin{array}{cccc} 1 & 0 & 4 & 0 \\ 0 & 1 & 5 & 0 \\ 0 & 0 & -22 & 0 \end{array} \right)\] [/math] then to this [math] \[ \left( \begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{array} \right)\] [/math] and so therefore the subset \beta is a basis for P2 hmmm i am not really sure that is right, anyways thats what i did, any help/comments would be welcomed!

hey i was just wondering how you show this... or well if i am doing or done it right? thanks -Sarah ...i'll post my answer in a min, just let me type it up...

or do you simply add the two formulas together? (by that i mean add the energy lost through conducion + energy lost through radiation)...but then i suppose...aghhh head imploding!!!

hmmm i can't quite see how to do this using both formulas...

reservoir?

ok so here is my updated answer... this the 'net' heat radiated by the person isn't it? also the question could be a trick one (so that the heat radiated = heat absorbed)????

or do you think when it says a room at the same temperature, that it means the room is at a constant temperature thoughtout it?