###### Asked in Math and ArithmeticAlgebraAbstract Algebra

Math and Arithmetic

Algebra

Abstract Algebra

# What is order of the resultant matrix AB when two matrices are multiplied and the order of the Matrix A is m n order of Matrix B is n p Also state the condition under which two matrices can be mult?

## Answer

###### Wiki User

###### August 14, 2011 7:45AM

the order is m p and the matrices can be multiplied if and only if the first one (matrix A) has the same number of columns as the second one (matrix B) has rows i.e)is Matrix A has n columns, then Matrix B MUST have n rows.

**Equal Matrix:** Two matrices A=|Aij| and B=|Bij| are said
to be equal (A=B) if and only if they have the same order and each
elements of one is equal to the corresponding elements of the
other. Such as A=|1 2 3|, B=|1 2 3|. Thus two matrices are equal if
and only if one is a duplicate of the other.

## Related Questions

###### Asked in Abstract Algebra, Linear Algebra

### Can matrices of the same dimension be multiplied?

No. The number of columns of the first matrix needs to be the
same as the number of rows of the second.
So, matrices can only be multiplied is their dimensions are k*l
and l*m. If the matrices are of the same dimension then the number
of rows are the same so that k = l, and the number of columns are
the same so that l = m. And therefore both matrices are l*l square
matrices.

###### Asked in Algebra

### Define the condition number of a matrix?

Matrix
Condition NumberThe condition number for matrix
inversion with respect to a matrix norm k¢k of a square matrix
A is defined by∙(A)=kAkkA¡1k;
if A is non-singular; and ∙(A)=+1 if A is singular.
The condition number is a measure of stability or sensitivity of
a matrix (or the linear system it represents) to numerical
operations. In other words, we may not be able to trust the results
of computations on an ill-conditioned matrix.
Matrices with condition numbers near 1 are said to be
well-conditioned. Matrices with condition numbers much
greater than one (such as around 105 for a 5£5Hilbert matrix) are
said to be ill-conditioned.
If ∙(A) is the condition number of A , then ∙(A) measures a sort
of inverse distance from A to the set of singular matrices,
normalized by kAk . Precisely, if A isinvertible, and
kB¡Ak<kA¡1k¡1 , then B must also be invertible. On the other
hand, in the case of the 2 -norm, there always exists a singular
matrix B such thatkB¡Ak2=kA¡1k2¡1 (so the distance estimate is
sharp).

###### Asked in Math and Arithmetic

### Is it possible to multiply a 3 X 2 matrix and a 2 X 3 matrix?

The first matrix has 3 rows and 2 columns, the second matrix has
2 rows and 3 columns.
Two matrices can only be multiplied together if the number of
columns in the first matrix is equal to the number of rows in the
second matrix.
In the example shown there are 3 rows in the first matrix and 3
columns in the second matrix. And also 2 columns in the first and 2
rows in the second.
Multiplication of the two matrices is therefore possible.

###### Asked in Algebra, Abstract Algebra, Linear Algebra

### Is a singular matrix an indempotent matrix?

A singular matrix is a matrix that is not invertible. If a
matrix is not invertible, then:
• The determinant of the matrix is 0.
• Any matrix multiplied by that matrix doesn't give the identity
matrix.
There are a lot of examples in which a singular matrix is an
idempotent matrix. For instance:
M =
[1 1]
[0 0]
Take the product of two M's to get the same M, the given!
M x M = M
So yes, SOME singular matrices are idempotent matrices!
How? Let's take a 2 by 2 identity matrix for instance.
I =
[1 0]
[0 1]
I x I = I obviously.
Then, that nonsingular matrix is also idempotent!
Hope this helps!

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