I am stuck on a project, and am desperate for help. My teacher denied me any help during class, so I'm kind of packed into a corner.
1. I have to write an augmented matrix using this system : 2x=5y 3y+x=-11
2.After I find the augmented matrix, I have to find two matrices that multiply to a product of the augmented matrix.
Get the equations in general form:
The augmented matrix is just an array of all the numbers
in the system without the letters or equal signs:
That's a 2x3 matrix.
To find two matrices that have a 2x3 matrix as their
product, the first could be a 2x2 and the second a 2x3
matrix.
Let's make up an arbitrary 2x2 matrix, say
Then we'll let the 2x3 matrix be:
So we have
Equating elements of the two 2x3 matrices:, we have
these 3 systems of equations:
, , ,
We solve those 3 systems and get p=1,s=0, q=-1,t=-1,r=-3,u=2
So one possible answer is
But you could make up any (non-singular) 2x2 matrix
and find a 2x3 matrix so that the product would be
equal to the augmented matrix. There are many possible
answers, in fact infinitely many.
Edwin