Just use the formula twice (on each of those products). Start with [tex]((AB)C)_{ij}=\sum_k(AB)_{ik}C_{kj}.[/tex] Now use the formula again to evaluate [itex](AB)_{ik}[/itex].P-Jay1 said:A is an M × N matrix, B is N × K and C is a K × L matrix. Consider matrix
multiplication (AB)ij = Pk AikBkj .
Using the formula, (AB)ij = Pk AikBkj, how would I calculate ((AB)C) and (A(BC))?
Matrix multiplication is a mathematical operation where two matrices are multiplied together to produce a new matrix. It is different from regular multiplication as it follows a specific set of rules and involves multiplying every element of one matrix with every element of the other matrix.
Matrix multiplication involves multiplying the rows of the first matrix with the columns of the second matrix and adding the products. The result is a new matrix with the number of rows from the first matrix and the number of columns from the second matrix. This operation can only be performed if the number of columns in the first matrix is equal to the number of rows in the second matrix.
The rules for matrix multiplication are:
Matrix multiplication is an important operation in linear algebra as it allows for the representation and manipulation of linear equations and systems. It is also used in many fields such as computer graphics, physics, and economics, to name a few.
Matrix multiplication involves multiplying two matrices together, while scalar multiplication involves multiplying a single matrix by a constant number. Matrix multiplication follows a specific set of rules, while scalar multiplication is simply multiplying every element of the matrix by the scalar value. Additionally, the result of matrix multiplication is a new matrix, while the result of scalar multiplication is still the same size matrix as the original matrix.