Recent content by boings

You're right, I should know that basic property :) I've been cramming too much this semester so I tend to forget. Thanks a lot it makes good sense.

Perhaps the very beginning is where I'm having trouble, I don't know what times a matrix would be equal to zero. Is it the transpose? Or perhaps a matrix whose determinant is zero?

Homework Statement I have attached the relevant question as an image (for sake of ease) Homework Equations The Attempt at a Solution Also attached, in blue. Thanks a lot for any help at all!

Actually, can you help me out with the last steps for solving? I'm still a bit caught up. I attached my attempt where you left off. thanks

Oh I see, that was easier than I thought. I always get tripped up when they mention matrices and think that I have to tread very cautiously. thank you

Homework Statement Let A\inM_{n}(\Re) a matrix verifying A^{3}-A^{2}-I_{n}=0 a) Show that A is inversible and calculate it b) Show that the solution X\subsetM_{n}(\Re) of the equation A^{k}(A-I_{n})X=I_{n} has a unique solution. The Attempt at a Solution I'm having...

What should this be exactly? I'm not sure I understand either

Oh ok I get it! thank you so much. I see how that's not a line now, but rather the equation that relies the orthogonality between AI and BI. It sure looks like a a parametric equation of a line though ^^ thanks again

Alrighty, so I then get (4-2k, -2-2k, -14 - 4k)=0 which represents the line AI. This is where I get a little tripped up. Should I solve for k and replace into original equation of the line? The answer should be: A(-3, -4, -4)

Hi and thanks! good point! (if k=constant) x= 0 + k y= -1 + k z= 2 + 2k Although, when I plug that in it doesn't make much sense. I proceed like this: AI (dot) BI = (-2, 2, 2)(dot)(-2, -2, -5)(0 + k, -1 + k, 2 + 2k) I think that this is already flawed in some sense

Homework Statement We consider two points, B and I and a line 'a'. B(0,-4,-7) I(-2,-2,-5) and a: x = y+1 = (z-2)/2 Determine the summits of A and C of triangle ABC knowing that: -Summit A belongs to the line 'a' -I is the foot of the height from A (perpendicular to BC) -The...

You're right, I'm going to take your word and their word on this and not lose any sleep over whether it will be useful to me :) thanks

thanks a lot, that's a great reply. So if commutativity in this case were to be proven, has it been referenced also as "mixed commutativity"?

right, that is pretty intuitive isn't it. Could a line segment divide a number line into uneven parts? Considering the line segment is finite

Hah, yeah I thought that was wrong, but couldn't find the right one, thanks! So am I correct in saying that the scalar operation on a vector space is commutative and associative? thank you both