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No worries. Feel free to shotgun me in the mouth if I had taught you something wrong. :)

Fair enough. Then you must have concluded that r = P + sQ + tQ and NOT r' = P+ su + tv because r has Cartesian equation x+2y-z = 2. However P(1,0,1) does satisfy it. The point is that you did the right working out for a) saying that r = r0 + su + tv but you wrote down r = r0 + sv + tw where v...

P = (1,1,1), Q = (1,0,1), R = (0,2,2) u = Q - P = (0,-1,0) v = R - P = (-1,1,1) Then, r = r0 + su + tv = r0 + s(0,-1,0) + t(-1,1,1) which is not r = (1,1,1)+s(1,0,1)+t(0,2,2)????? _____ Anyway, I'm not doing the computation. If you did similar to my explanation to b), then it's right...

Feeling sympathetic... _________________ I got w = (-1, 2, -1). If you understand what b) meant, then you should understand what c) meant. The volume of a parallelpiped defined by u, w, v is V = u ⋅ (w x v). The volume of a parallelpiped defined by w-u, u, v is V' = (w-u) ⋅ (u x...

So you found a strategy that yields impressive grades but has an immense drawback that you know will kill you in the future as mathematics is like building a tower, you can't go far with a weak foundation. I believe the problem with your strategy is that you believe too strongly of grades. It's...

Good but r=(1,1,1) + s(1,0,1) + t(0,2,2) = r0+sQ+tR != r0+su+tv.

I haven't done any computations but could you explain how you got r=(1,1,1) + s(1,0,1) + t(0,2,2) because this disagrees with my understanding of planes. Sorry for the backtrack just making sure.

There's no LaTeX present. Hint for (c) is "what condition is required for 2 vectors to be orthogonal?" and (d) Euclid

Do it yourself, mate. You're too worried about how to do these questions and whether it's something that you need to learn rather than exercising your problem solving skills. Here I demonstrate Q3 (a), which you CAN do. What is the structure of a cartesian equation in R3? ax+by+cz=d, where...

Thermal cracking is expensive and inefficient (i.e., cost:benefit ratio is too high). This is the result of the great amounts of heat energy required to continually perform this process. On the other hand, catalytic cracking is significantly more efficient and less costly due to the presence...

It seems that there is no t such that the system yields infinite solutions.

If you want to get infinite solutions, then you need to prevent at least one row from giving any information. Intuition: for RREF, each row should give information about one of x, y, or z. But when you stop one row from finding either x, y, or z, then you won't be able to solve other rows. e.g...

Suppose you had a row like this: (0 0 0 | 2317). Would it make sense?

Do row operations as usual, group up the rows containing t to make it easier to analyse.: \begin{align*} (A|b) = \left(\begin{array}{ccc|c} t & -5 & 3 & -8t \\ -t & 8 & 3t & 11t \\ -1 & 2 & 3 & 1\end{array}\right) \stackrel{R1 \leftrightarrow R3}\longrightarrow &...

Re: HSC 2017 MX2 Marathon The book's answer is right, you can check it by squaring it to get 5 + i.

Gaussian elimination.

My heart is accelerating at a dangerous rate. Stop it.

I think you should dedicate more focus to your HSC rather than playing some joke with sabbabbby.

Why?

You could use mathematical induction.