Recent content by mattyk

Good point. I'll have to remember that.

Homework Statement I was given this question as a part of an assignment and lost a mark because of a step.Homework Equations the integral of cos^5(x) dx after some fiddling and substitution it gets to this (1 - u^2)^2 du In the solutions there is a step that says refine = (u^2 - 1)^2...

Just to make sure I have this right I go on to work out c1(1, 2, 1, 1) + c2(1, 3, 0, 2) + c4(2, -1, 0, 1) = (1, 1, 2, 0) and c1(1, 2, 1, 1) + c2(1, 3, 0, 2) + c4(2, -1, 0, 1) = (5, -5, -1, 2). And this shows that c3 and c5 are linear combinations of c1, c2 & c4?

Just to make sure I have this right I go on to work out c1(1, 2, 1, 1) + c2(1, 3, 0, 2) + c4(2, -1, 0, 1) = (1, 1, 2, 0) and c1(1, 2, 1, 1) + c2(1, 3, 0, 2) + c4(2, -1, 0, 1) = (5, -5, -1, 2). And this shows that c3 and c5 are linear combinations of c1, c2 & c4?

Homework Statement A= \begin{bmatrix} 1 & 1 & 1 & 2 & 5 \\ 2 & 3 & 1 & -1 & -5 \\ 1 & 0 & 2 & 0 & -1 \\ 1 & 2 & 0 & 1 & 2 \end{bmatrix} Homework Equations I get this RREF \begin{bmatrix} 1 & 0 & 2 & 0 & 0 \\ 0 & 1 & -1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0...

As far as I can work out it is right but it just seems too simple.

Homework Statement U(1, -1, 2) V(0, 3, -1) W(-1, -1 1) Calculate ||(U + V + W) Homework Equations is it as simple as U + V + W then finding out the magnitude of that point. The Attempt at a Solution [/B] For example (U + V) + W then the magnitude of that point?

I wrote the original equation down wrong. it should be -2x1 - 5x2 + x3 = b1. Sorry about the mistakes. I'll try to be more careful in the future. And thank you once again for your help, it has been invaluable. It really helped me get my head something I was struggling to grasp.

Dang it. I looked at that so many times. So changed I get x1 + 2x3 = -5b1 - 3b2 x2 - x3 = 2b1 + b3 0 = 7b1 + b2 + 4b3

I've had another go with what @HallsofIvy has posted. [1 3 -1 | b1 ] [1 -1 3 | b2 ] [-2 -5 1 | b3 ] [1 3 -1 | b1 ] [0 -4 4 | b2 - b1 ] R2 - R1 = R2 [0 1 -1 | b3 + 2b1 ] R3 + 2R1 [1 3 -1 | b1 ] [0 1 -1 | b3 + 2b1 ] Swap R2 & R3 [0 -4 4 | b2 - b1 ] [1 0 2 | b1 - 3(b3 + 2b1) ] R1 - 3R3 [0 1 -1...

Or not. I think I get it now. I replied at 2am whilst trying to feed a 1 year old.

Thanks for your reply. I've written the question down wrong. A copy and paste error. Sorry about that. It should be x1 + 3x2 - x3 = b1 x1 - x2 + 3x3 = b2 -2x1 - 5x2 - x3 = b3 I'm assuming that changes things.

I have x1 + 3x2 - x3 = b1 x1 - x2 + 3x3 = b1 -2x1 - 5x2 - x3 = b1 So using an augmented matrix I get this [1 3 -1 | 1] [1 -1 3 | 1] [-2 -5 1 | 1] [1 3 -1 | 1] [0 -4 4 | 0] R2 - R1 = R2 [0 1 -1 | 3] R3 + 2R1 = R3 [1 3 -1 | 1] [0 1 -1 | 3] Swap R2 with R3 [0 -4 4 | 0] [1 0 2 | -8] R1 - 3R2 =...

So the title sums up who I am right now. I've been a primary teacher for a few years and I am taking a few years off to be the stay at home dad and I thought I'd retrain to become a high school mathematics teacher. Successfully made it through the first semester and I'm now half way through...