How to Multiply Matrices

Multiplying matrices is painless when you understand the method described here.

Instructions

  • Step 1: Check rows and columns Makes sure the number of columns in the first matrix equals the number of rows in the second.
  • TIP: Unless the number of columns in the first matrix equals the number of rows in the second, their product will be undefined.
  • Step 2: Calculate the (row 1, column 1) entry Place the sum of the products from row 1 of the first matrix and column 1 of the second matrix in the (row 1, column 1) position of the product matrix.
  • Step 3: Calculate the (row 2, column 1) entry Place the sum of the products from row 2 of the first matrix and column 1 of the second matrix in the (row 2, column 1) position of the product matrix.
  • Step 4: Calculate the remaining entries Continue multiplying the elements of the rows of the first matrix by the elements of the columns in the second matrix until you have formed a product matrix with the dimensions of (rows of the first matrix) by (columns of the second matrix).
  • FACT: The word matrix comes from the Latin word for mother.

You Will Need

  • Compatible matrices
  • Calculator

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