Posted by Deborah on Friday, November 23, 2012 at 10:06pm.
If we denote the system of linear equations in matrix form as:
L y = x (1)
where y = (y1,y2,y3,...) are the variables you want to solve for, then L being a linear operator, you have that:
L (a y+ bz) = a L y + b Lz
So, if y and z are two different solutions to (1), you have:
L (ay + bz) = (a + b) x
Therefore:
L[(ay+ bz)/(a+b)] = x
So, given two different solutions y and z, you can construct an infinite number of others by taking arbitrary linear combinations of the two.
A system of linear equations is represented by 2 straight lines
These two lines can
1. intersect at one point ---> one solution
2. be 2 distinct lines parallel to each other ---> no intersection
3. be the same line ----> infinite number of solutions
But two straight lines could not possibly intersect at 2 points, so your correct choice is C
I thought B.
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