21.3.3. Matrix Multiplication

Try these first

1. 1.

   Is matrix multiplication commutative? Give an example.

   Hint

   Think about multiplying two matrices and their orders.

2. 2.

   What is the product of a 2x3 matrix and a 3x2 matrix called?

   Hint

   Recall the resulting dimensions based on matrix multiplication rules.

3. 3.

   Is matrix multiplication commutative?

   • True
   • False

   Hint

   Think of a basic example to illustrate.

4. 4.

   If A is a 3x2 matrix and B is a 2x4 matrix, what will be the dimensions of the resulting matrix AB?

   • 3x2
   • 3x4
   • 2x3
   • 2x4

   Hint

   Focus on the outer rows and columns of A and B.

5. 5.

   Prove that matrix multiplication is associative. Let A, B, and C be matrices of compatible dimensions.

   Hint

   Start with the definition of matrix multiplication and examine the resulting elements.

6. 6.

   If A is a 2x2 matrix and B is a 2x3 matrix, derive the general formula for the elements of the product AB.

   Hint

   Remember how to compute dot products for each row and column.