How would I calculate the coordinates x1, x2, x3, x4 for the vector x?
#Linear Algebra: Matrix multiplication!
dim knoll
tepid pikeBOT
dim knoll
I thought of this approach, but wouldn't know how to continue...
dim knoll
Just use row operations to get to row echelon form
Yes, but this matrix seems a bit different as it is not a square matrix (m = n)
hazy olive
Ah I didn’t see
Hm
You can just try to brute force it ig?
With normal system of lin eq solving
dim knoll
I wouldn’t know how to do that
molten torrent
You can do gaussian elimination when you don't have square matrices
blazing moon
You can just try to brute force it ig?
Isn't that impossible? You'd have a system of 3 equations with 4 variables...
hazy olive
No, you have some 0s
molten torrent
So you should end up with at least a 1-dimensional solution space.
molten torrent
Just depending on how many free variables you have leftover.
dim knoll
You can do gaussian elimination when you don't have square matrices
I could solve it to this point
dim knoll
x_3 and x_4 can be anything you want
What would be the next step for this?
molten torrent
That's the solution.
You'd write it as $\begin{bmatrix}2-2x_{3}-3x_{4}\1-3x_{3}-2x_{4}\x_{3}\x_{4}\end{bmatrix}$
supple coralBOT
Riesz Rambutan Theorem
molten torrent
Any values of $x_{3}$ or $x_{4}$ you pick would work.
supple coralBOT
Riesz Rambutan Theorem
dim knoll
You'd write it as $\begin{bmatrix}2-2x_{3}-3x_{4}\\1-3x_{3}-2x_{4}\\x_{3}\\x_{4}...
Where does the first number come from first row: 2 and second row: 1?
molten torrent
I could solve it to this point
What this is saying is that $x_{1}+2x_{3}+3x_{4}=2$ and $-x_{2}-3x_{3}-2x_{4}=-1$.
supple coralBOT
Riesz Rambutan Theorem
dim knoll
What this is saying is that $x_{1}+2x_{3}+3x_{4}=2$ and $-x_{2}-3x_{3}-2x_{4}=-1...
Okay, I see
dim knoll
What this is saying is that $x_{1}+2x_{3}+3x_{4}=2$ and $-x_{2}-3x_{3}-2x_{4}=-1...
I'd also do the second part of the task
molten torrent
That's sort of what I did.
dim knoll
That's sort of what I did.
Now I get the point. Thanks for clarifying! 👍
dim knoll
That's sort of what I did.
How would I go for this?
molten torrent
Calculate $A\begin{bmatrix}x_{1}\x_{2}\x_{3}\x_{4}\end{bmatrix}$. It should be a length-3 vector. Then work out $A\begin{bmatrix}x_{1}\x_{2}\x_{3}\x_{4}\end{bmatrix}=\begin{bmatrix}0\0\0\end{bmatrix}$.
supple coralBOT
Riesz Rambutan Theorem
dim knoll
Calculate $A\begin{bmatrix}x_{1}\\x_{2}\\x_{3}\\x_{4}\end{bmatrix}$. It should b...
So is it basically the same as the previous task?
molten torrent
All of undergrad LA is basically matrix multiplication or row-reduction.
dim knoll
What does undergrad LA mean?
molten torrent
Undergrad linear algebra.