Objective
To multiply matrices using scalar and matrix multiplication
In the Solve It, you may have found the sum of products. Finding the sum of products is essential to matrix multiplication.
Essential Understanding The product of two matrices is a matrix. To find an element in the product matrix, you multiply the elements of a row from the first matrix by the corresponding elements of a column from the second matrix. Then add the products.
Before you learn how to multiply two matrices, however, you should learn a simpler type of multiplication. This type of multiplication allows you to scale, or resize, the elements of the matrix.
The real number factor (such as 3 in the example) is a scalar. Multiplication of a matrix A by a scalar c is scalar multiplication. To find the resulting matrix cA, you multiply each element of A by c.
To multiply a matrix by a scalar c, multiply each element of the matrix by c.