division is possible in matrix.?

Question

A and B are two matrix A/B is possible?.

Answer 1

In a sense, yes it is possible. But a great amount of care is needed when doing something like this. The idea is to think of division as multiplication by an inverse. First of all, B has to be a square matrix. Second, the determinant of B must be non-zero so that B^(-1) exists. Finally, care must be taken since it is likely that A[B^(-1)] and [B^(-1)]A are different matrices. Both of these matrices could be thought of as the quotient of A and B. The particular problem would dictate which is needed.

Answer 2

There is not in general matrix division, only if the matrix in question has an inverse. Division is only possible where the number being divided by has an inverse. This is why you cannot divide by 0, in the field of the real numbers (if you know what "field" means), 0 has no multiplicative inverse, so you cannot divide by it. Multiplication by 0 is defined but not division - similarly, multiplication is defined on all square matrices, but division only for those with inverses (that is, B is the inverse of A if AB = BA = I, the identity matrix)

Answer 3

If B has either the same number of rows or the same number of columns as A, then this may be possible, and could be solved with a series of equations (itself represented as a matrix). However, if the other dimension of B (the one not equal to that of A) is greater than that of A, you have more unknowns than you have equations, and you will have infinitely many solutions, controlled by some number of independent parameters. If the other dimension of B is greater than that of A, you have too many equations, and no guarantee that they are not contradictory, so you may have no solution. If both matrices are square and of equal order, and A has a non-zero determinant, you should be able to get a single solution.

Answer 4

division is possible in matrix but in reverse way, only if both matrices are of same order.
suppose we want A/B, both are matrices.
now we can assume the result matrix to be C.
hence A/B = C
=> A = B*C
we can equate terms in product of B*C to the corresponding terms in A,
from this we get equations which upon solving give the terms of C. hence the result

Answer 5

No, not as you have it written. Matrix multiplication is NOT commutitive in general, that is AB ≠ BA.

But you can multiply be the inverse and affect the desired result:

suppose:

AB = C

the inverse of A is Aˉ¹, so

Aˉ¹AB = Aˉ¹C
B = Aˉ¹C

if you had:

ABC = D

and you wanted to find C:

C= Bˉ¹Aˉ¹D

that is you MUST perform the multiplication in that order.

Answer 6

yes it's possible
but No. of rows in both matrices(the order of the matrix) should be the same

Answer 7

C = A/B
can eb re-arranged A = C*B
Let B' be ithe inverse of B such that B*B' = the unity matrix
Then A*B' = C*B*B' = C
So A/B is really A*B'

Answer 8

absolutely possible only when number of culomns in A is equal to number of rows in B invers

Answer 9

A/B is possible it is AB^(-1) but under certain conditions

Answer 10

no division is not possible in maths