Find the matrix X such that XA=B ..?
A = ((3a, 2b),(-a,b))
Above is a single matrix A shown.
B = (( -a , b ),(2a, 2b))
Above shown is a single matrix B.
Above is a single matrix A shown.
Above shown is a single matrix B.
1 Answer
Here is another way to do this. We write
XA = B ,
and
[(x_1,x_2),(x_3,x_4)][(3a,2b),(-a,b)] = [(-a,b),(2a,2b)] .
From matrix multiplication, we obtain the following system of equations:
3ax_1-ax_2 = a(3x_1 - x_2) = -a " "" "bb((1))
2bx_1 + bx_2 = b(2x_1 + x_2) = b " "" "" "bb((2))
3ax_3 - ax_4 = a(3x_3 - x_4) = 2a " "" "" "bb((3))
2bx_3 + bx_4 = b(2x_3 + x_4) = 2b " "" "" "bb((4))
From
3x_1 - x_2 = -1
=> x_1 = x_2/3 - 1/3
From plugging
2(x_2/3 - 1/3) + x_2 = 5/3 x_2 - 2/3 = 1
=> x_2 = 1
=> x_1 = 0
From
3x_3 - x_4 = 2
=> x_3 = 2/3 + x_4/3
From plugging
2(2/3 + x_4/3) + x_4 = 5/3x_4 + 4/3 = 2
=> x_4 = 2/5
=> x_3 = 12/15 = 4/5
Therefore,
color(blue)(X = [(0,1),(4/5,2/5)])
[(0,1),(4/5,2/5)][(3a,2b),(-a,b)] = [(-a,b),(2a,2b)] .