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OK finding 1 solution was fine and dandy and all...but...how do we go about finding other solutions since the system has infinitely many solutions? Is there algebra we can use to generate other solutions? An equation maybe🤔?
The equation is r=s(-5,1,1,0)+t(-8,2,0,1) where r is the 4 dimensional vector corresponding to the solution and the brackets are 4x1 matrices. I don't know if a Cartesian equation is possible because you can't use the cross product.
Like it’s shown in the video, if you let s and t be any real numbers and use the formula I derive then the resulting 4-dimensional vector will be a solution. Since you can let s and t be any real numbers, you get an infinite number of solutions. Edit: looks like another viewer has already filled in the details of what I wrote above.
