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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.

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Q: 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?
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How do you know if two matrices can actually be multiplied?

The number of columns in the first matrix must equal the number of rows in the second.

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.

What is the singular form of matrices?

The singular form of matrices is matrix.

22 matrix with 33 matrix multiplication?

It is not possible. The number of columns in the first matrix must be the same as the number of rows in the second. That is, matrices, X (kxl) and Y (mxn) can only be multiplied [in that order] if l = m.

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No. Only square matrices can be triangular.

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What is the determinant rank of the determinant of 123456 its a 2 x 3 matrix?

A determinant is defined only for square matrices, so a 2x3 matrix does not have a determinant.Determinants are defined only for square matrices, so a 2x3 matrix does not have a determinant.

When is it important for a matrix to be square?

In the context of matrix algebra there are more operations that one can perform on a square matrix. For example you can talk about the inverse of a square matrix (or at least some square matrices) but not for non-square matrices.

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

Why rectangular matrix have no inverse in linear algebra?

Inverse matrices are defined only for square matrices.

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.

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