6.5.1. Pseudo Code

Try these first

1. 1.

   What is required for two matrices A and B to be multiplicable?

   Hint

   Think about the dimensions of both matrices.

2. 2.

   Explain what is meant by the cost of matrix multiplication.

   Hint

   Consider how many operations are needed to calculate the entries.

3. 3.

   What must be true for two matrices A and B to be multiplied?

   • A's rows should equal B's columns
   • A's columns should equal B's rows
   • A's rows and columns must be equal

   Hint

   Analyze the matrix dimensions carefully.

4. 4.

   Matrix multiplication is commutative.

   • True
   • False

   Hint

   Consider how switching two matrices changes the product.

5. 5.

   Given matrices A(5x10), B(10x3), and C(3x8), calculate the total operations for both (AB)C and A(BC). Which order is more efficient?

   Hint

   Use the dimensions to derive the number of operations required explicitly.

6. 6.

   Imagine you have four matrices of varying dimensions. Devise an algorithm to compute the most operationally efficient multiplication order. Write the pseudo-code.

   Hint

   Think in terms of breaking down the problem into smaller segments and compute their costs recursively.