Recent content by Jundoe

This is clear. But I fail to understand why it would need to be reflected first before being rotated. (Note that I'm visualizing this with a paper as an object, and my desk as the space). If I draw an imaginary x=y line and rotate it before I reflect it, I feel like the outcome would be the...

The problem asks to find the standard matrix for the composition of these two linear operations on R2. - A reflection about the line y=x, followed by a rotation counterclockwise of 60o. This is how I proceeded. y=x $\begin{bmatrix}0&1\\1&0 \end{bmatrix}$ counter clockwise 60degs...

Re: upper triangular matrix Just tried it out. This is much better than doing it by reaching an upper triangle. I don't know which is faster, but for my final I'm definitely going with this method. It's less error-prone. :D Thanks!

Re: upper triangular matrix This is intriguing. How would I proceed? Would I have to multiply the [4x4]matrix by some [4x3]matrix, then take the new [4x3] result and have it multiplied like so: [3x4][4x3], thus yielding a [3x3]? ...a google search only offered programmer contents.

Re: upper triangular matrix Actually this was an example. I was trying to understand this for a larger matrix seeing as my final will request I find the determinant of a 4x4. *I must've missed that vital information from my textbook–again, thanks EVERYONE for your inputs. That said, when it...

I want to make an upper triangular matrix. From this: $\begin{bmatrix}2&0&1\\0&1&1\\3&1&0 \end{bmatrix}$ The first is the correct one. The second is incorrect, yet I fail to understand why. $\begin{bmatrix}2&0&1\\0&1&1\\3&1&0 \end{bmatrix}$ $\begin{bmatrix}2&0&1\\0&1&1\\0&1&-3/2...

Much clearer, thank you. I was aware of assigning free variables yet, for some odd reason, thought the zeroes were pretty much obsolete, and would ignore them instead of assigning them a variable.

I'm facing some doubts regarding the parametrization of a given matrix. Let's say, the following matrix is reduced. From: $\begin{bmatrix}0 & 2 & -8\\0 & 2 & 0\\0 & 0 & 2\end{bmatrix}$ To: $\begin{bmatrix}0 & 1 & 0\\0 & 0 & 1\\0 & 0 & 0\end{bmatrix}$ To Parametrize that I would do the...

Thank you for replying! So in other words, the position of the vector–its origin–is irrelevant in this matter? So, ignoring the point. I would have the following: w1= 1/2(3,-2,1) w2= (3,2,2)-1/2(3,-2,1)= (3/2, 3, 3/2) Hope I didn't do any careless mistakes, does that seem about right?

I would like to verify this problem from an introductory to Linear Algebra course. It goes as follows: This is how I proceeded: From the given parametric equations I constructed the vectors: line L: a=(3, -2, 1) and b=(2,1,-2). To find w1, I know that w1= kL And to find k: (v.L)/||L||2 And...