Question

How do you multiply matrices of different sizes?

Answer 1

The given question is related to the concept of matrices. In order to understand this question, we must first know the concept of matrices. An ordered rectangular array of numbers be it real or complex numbers or functions is known as a matrix. There are three basic terms related to the concept of matrices that are- elements, rows and columns of matrix.

Complete answer:
Matrices are used to represent coefficients in a system of linear equations. Elements of matrix are the numbers or the functions in the array. The rows of the matrix refer to the horizontal lines of elements while the columns of matrix refer to the vertical lines of elements. If any matrix has ‘m’ rows and ‘n’ columns, then the order of the matrix is $m \times n$.

Matrices of different sizes can only be multiplied if and only if the number of columns of the first matrix is equal to the number of rows of the second matrix. If not, then it is impossible to multiply the matrices of different sizes.

Therefore, row $\times$ column.

Note: The given question was merely theoretical, but it can only be understood if the concept of matrices is crystal clear to the students. There are different types of matrices such as scalar matrix, null matrix or square matrix and many more. Matrix multiplication only works when the number of columns of the first matrix is equal to the number of rows of the second matrix.