CoCalc Public FilesExtra DQ 1.ipynbOpen with one click!
Author: Richard Ketchersid
Views : 69
Description: Example showing two interpretations of Mx = b.
Compute Environment: Ubuntu 20.04 (Default)
In [2]:
x,y,z,t = var('x,y,z,t') M = matrix([[1,2,3],[2,-3,1],[1,1,0]]) v = matrix([x,y,z]).transpose() F = M*v p = matrix([1,1,1]).transpose() b = M*p

This first example shows the interpretation of the system Mx=bM\mathbf{x}=\mathbf{b} as the intersection of planes where [123231110][xyz]=[602]\begin{bmatrix}1&2&3\\2&-3&1\\1&1&0\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}6\\0\\2\end{bmatrix} is viewed as a system of equations

(Share server only supports KaTeX; open in CoCalc to see this formula.)
The solution here is x=1,y=1,z=1x=1, y=1, z=1

In [3]:
G = implicit_plot3d(F[0][0] == 6, (x,-4,4), (y, -4,4), (z, -4, 4), color='green', opacity='0.9', aspect_ratio=[1,1,1]) G += implicit_plot3d(F[1][0] == 0, (x,-4,4), (y, -4,4), (z, -4, 4), color='red', opacity='0.9') G += implicit_plot3d(F[2][0] == 2, (x,-4,4), (y, -4,4), (z, -4, 4), color='blue', opacity='0.9') G += sphere((1,1,1), size=.1, color='yellow', opacity='1') G.show(fig_size=4)