If A and B are matrices of order m×n and n×n respectively, then which of the following are defined ?
Answers
If A and B are matrices of order m×n and n×n respectively, matrix addition, scalar multiplication and transpose of A and B are defined.
There are a few different operations that can be performed with matrices, and whether or not they are defined depends on the specific dimensions of the matrices involved.
Matrix addition: If A and B are matrices of the same order, then matrix addition is defined. A+B is a matrix of the same order as A and B.
Scalar multiplication: Scalar multiplication is defined for any matrix A, it can be multiplied by any scalar value, the resulting matrix will have the same order as A.
Matrix multiplication: If A is a matrix of order m×n and B is a matrix of order n×p, then matrix multiplication is defined. The resulting matrix is of order m×p.
Transpose: Transpose of any matrix A is defined and it can be denoted by A' or AT, the order of A' is nxm if A is of order mxn.
Inverse: If A is a square matrix (i.e. m×m) and it is invertible, then the inverse of A is defined and it can be denoted by A^(-1).
Determinant: Determinant of any square matrix is defined and it is denoted by |A| or det(A).
Matrix multiplication of A and B is defined and the resulting matrix is of order m×n. Inverse and Determinant of B are defined as B is square matrix.
To know more about matrices visit : https://brainly.in/question/41163122
https://brainly.in/question/16155995
#SPJ1