Matrices division is not possible because of the following reasons:-
In case of matrices one difference is that they are commutative when added but they are not always commutative when they are multiplied. So for two real numbers, x and y
xy = yx,
always.
But for two
matrices, A and B,
Usually AB ≠
BA
Another is that, while every non-0 real number has a multiplicative inverse (reciprocal), not every non-0 matrix has an inverse. And mathematically speaking, division by x consists of multiplication by the inverse of x.
So if we wanted to divide matrix A by matrix B, we first have to find the inverse of B which may or may not exist. But even if it does exist because of that non-commutativity thing in multiplication about the matrices, you have two ways to multiply it onto A:-
Another is that, while every non-0 real number has a multiplicative inverse (reciprocal), not every non-0 matrix has an inverse. And mathematically speaking, division by x consists of multiplication by the inverse of x.
So if we wanted to divide matrix A by matrix B, we first have to find the inverse of B which may or may not exist. But even if it does exist because of that non-commutativity thing in multiplication about the matrices, you have two ways to multiply it onto A:-
A x B˜¹
or
B˜¹ x A
or
B˜¹ x A
and those
will ordinarily be different.
Conclusion:-
So due to the various reasons mentioned above the idea of dividing the two matrices just does not work well when applied to matrices.
So due to the various reasons mentioned above the idea of dividing the two matrices just does not work well when applied to matrices.
ok
ReplyDelete