Multiplication of Matrices

Notes, Lesson 6.3 Multiplication of Matrices

Scalar Multiplication and Matrix Addition were mostly intuitive. If I had asked you to predict how those two operations would have been done, you probably would have guessed correctly how they would be done. Matrix Multiplication is not so intuitive and must be carefully be considered.

Definition:

Matrix Multiplication

Corresponding elements in that row of the first matrix are multiplied with the corresponding element of that column of the second matrix, and then added.

Requirement:

In order to be able to multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix.

Observation:

The answer matrix to a matrix multiplication will always have the number of rows of the first matrix, and the the number of columns in the second matrix. OR If an mxn matrix is multiplied by an nxr matrix, the answer matrix will be an mxr matrix.

Sample Problem #1.

	Given Problem.
	Corresponding elements in that row of the first matrix are multiplied with the corresponding element of that column of the second matrix, and then added.
	Simplified.

Sample Problem #2.

	Given Problem.
	Corresponding elements in that row of the first matrix are multiplied with the corresponding element of that column of the second matrix, and then added.
	Simplified.

Me long ago with my teacher: (NO, NOT REALLY)