ANSWERS: 1
  • sigh...ok. stupid useless textbooks. take your matrix, and do gauss-jordan elimination to get it into reduced-row eschelon form (the one where there's a diagonal line of 1's and the rest all 0's). If there is at least one row in the bottom that is all 0's [0 0 .... 0 | 0], then there are infinite solutions. What this line says is that 0*x=0. Any value of x will satisfy this equality. Another possibility is [0 0 ... 0 | n] where n is a number other than 0. In this case, there is no solution. What this line says is 0*x=n. No value of x will satisfy this. If you're lucky, all your rows will be in the form [0 0...1...0 0 | n]. Then your system of equations has a single unique solution.

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