Matrix multiplication is a mathematical operation that takes two matrices as inputs and produces a new matrix as an output. It involves multiplying corresponding elements of rows and columns to obtain the elements of the new matrix.
The rules for matrix multiplication are as follows:
To multiply a matrix by a scalar (a single number), you simply multiply each element in the matrix by that number. For example, if we have a matrix A and want to multiply it by the scalar 2, the resulting matrix would be 2*A.
Yes, you can multiply a matrix by a vector. The vector should have a number of elements equal to the number of columns in the matrix. The resulting vector will have the same number of elements as the number of rows in the matrix.
The identity matrix is a special type of matrix that, when multiplied by any other matrix, results in the same matrix. It is an n x n matrix with 1s along the main diagonal and 0s in all other positions. For example, if we have a 3 x 3 identity matrix I and multiply it by a matrix A, the result will be A. The identity matrix serves as the multiplicative identity in matrix multiplication, similar to how the number 1 serves as the multiplicative identity in regular multiplication.