Linear algebra parameters?
If the reduced coefficient matrix of a consistent system of linear equations has 5 rows, 3 of which are zero, and 5 columns, how many parameters does the general solution contain?
Any help on how to solve this question will be greatly appreciated. What is the question asking for when its asking for parameters?
Comments
In a matrix, the # of parameters is the number of columns in the matrix. When you convert a word problem to a matrix, the columns represent your variables. I'm not sure what is meant by general solution, but if that's the same as a basis, then there are 2 parameters. This is because if you row reduce your matrix, since the bottom 3 rows are all zeros, you'll only end up with 1 (pivot points) in the first 2 columns. Note that it would be possible for the 1st row to be a multiple of the 2nd row, so the 2nd row could cancel out and you'd only have 1 parameter and 4 free variables. So the answer is 1 or 2.
EDIT: I just noticed your question says "reduced" coefficient matrix, so the answer is 2.