How to Multiply Two Matrices

Step 1

In order to observe the two matrices that will be multiplied, we need to click on the image to see them. Remember, the number of columns in the first matrix must be equal to the number of rows of the second matrix. The size of the product matrix will have the number of rows of the first matrix and the number of columns of the second matrix (Note: a 2x3 matrix is a matrix with 2 rows and 3 columns). So, if we multiply a 2x3 matrix with a 3x3 matrix, the product matrix will be a 2x3 matrix. Please click on the Image for a better understanding. 

Step 2

The Matrix A has as its entries in the first row 3 1 2 and the Matrix B has in its first column the entries 1 1 -1. The first entry of the product matrix will be the sum of the products of the respective entries of the first row of Matrix A with the entries of the first column of Matrix B. That is, (3)(1)+(1)(1)+(2)(-1) = 3+1-2 = 2. Please click on the Image for a better understanding.

Step 3

The entry in the first row, second column, of the Product matrix is found by the sum of the products of the respective entries of the first row of Matrix A and the entries of the second row of Matrix B. That is, (3)(-1)+(1)(0+(2)(2) = -3+0+4 = 1. Please click on the Image of step #2 for a better understanding.

Step 4

The entry in the first row, third column, of the Product matrix is found by the sum of the products of the respective entries of the first row of Matrix A and the entries of the third row of Matrix B. That is, (3)(2)+(1)(3)+(2)(-1) = 6+3-2 = 7. Please click on the Image for step #2 for a better understanding. 

Step 5

Similarly we continue the process that we have done in steps #2,#3,and #4 to get the second row of the Product Matrix, that is,we take the sum of the Products of the respective entries of the second row of Matrix A and the entries of the first column, the second column, and the third column of the Matrix B in which we get the entries -1, 4, and 1.Please clcik on the image to see the Product Matrix.

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