/sci/ - Science & Math

>>12765220
You need to cancel them out because that's what Ax = 0 is asking you to do. If you write out all the matrix multiplications and set up your resulting equations, if x = [x1 x2] you get that

[math] -6x_1 + 9x_2 = 0[/math]
[math] 4x_1 + -6x_2 = 0[/math]
[math] -4x_1 + 6x_2 = 0[/math]

Or equivalently, if A1 is the left column of A, and A2 the right column, [math] x_1A_1 + x_2A_2 = 0[/math]. Therefore, [math] x_1A_1 [/math] must cancel out [math] x_2A_2 [/math] for that equality to hold. Your solution works, since if x1 = 1.5 & x2 = 1, every one of the above equations works out.

The 1 is there since the system is underdetermined, and you need to set x2 to some nonzero value (otherwise you get the trivial solution). Setting x2 to 1 is a good choice, since it makes finding x1 from any of the above equations pretty easy. Does that make sense?