2006-12-24 14:35:50 · 3 answers · asked by hans d 1 in Science & Mathematics ➔ Mathematics
well of course that statment is true.
the statement "A linear system SOMETIMES has at least one solution" can in fact be proved.
Just creat any linear system that has one solution and you will have proved it.
2006-12-25 04:21:09 · answer #1 · answered by travis R 4 · 0⤊ 0⤋
When the number of equations equals to the number of the unknowns then the linear system has a unique solution provided that the determinate of the coefficients matrix is not zero, means the system is linearly independent, more specifically the unknown vector defines a space.
Mathematically specking:
the linear system [A]{x}={b} has a unique solution when [A]/=0 and {b}/= infinity
2006-12-24 17:04:00 · answer #2 · answered by ws 2 · 0⤊ 0⤋
usually yes.. other possiblities include--- infinite solutions (same line in both equations) or no solution (lines never intersect)
2006-12-24 14:44:14 · answer #3 · answered by confused61394 1 · 0⤊ 0⤋