I am not sure what i am doing wrong in this question
Q. find a 2x2 matrix such that
|7 -4| |x y| |1 0|
|3 -1| * |z w|= |0 1|
I set it up like this
but whenever i solve for x and y i get an incorrect answer, not sure what i am doing wrong
7x- 4z= 1 and 3x- z= 0 so 12x- 4z= 0 and subtracting one equation from the other, 7x- 12x= -5x= 1 so x= -1/5.
Then 3x- z= -3/5- z= 0 so z= -3/5.
7y- 4w= 0 and 3y- w= 1 so 12y- 4w= 4. Subtracting, 7y- 12y= -5y= -4 so y= 4/5. Then 3y- w= 12/5- w= 1 so w= 12/5- 5/5= 7/5.
That's exactly the same answer as math2009 got.