Practice Matrix Multiplication - 6.1 | 6. Matrix Multiplication | Design & Analysis of Algorithms - Vol 3
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6.1 - Matrix Multiplication

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What must be true about the dimensions of two matrices A and B for them to be multiplied?

💡 Hint: Think about how many 'rows' one matrix can provide compared to the 'columns' of the other.

Question 2

Easy

What is the size of the resulting matrix when a 2x3 matrix is multiplied by a 3x4 matrix?

💡 Hint: Consider the rows of the first matrix and columns of the second.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

Which of the following statements about matrix multiplication is true?

  • Matrix multiplication is commutative
  • Matrix multiplication is associative
  • Matrix multiplication is both commutative and associative

💡 Hint: Think about whether you can swap the order of operations.

Question 2

If matrix A is 2x3 and matrix B is 3x4, what is the resulting matrix size of AB?

💡 Hint: Remember the rule for matrix multiplication sizes.

Solve 2 more questions and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given four matrices with dimensions 10x100, 100x5, 5x200, and 200x10, compute the minimum number of scalar multiplications needed to multiply them using a dynamic programming approach.

💡 Hint: Analyze the costs of different groupings like (AB)(CD) compared to A(BCD).

Question 2

Propose and analyze a new recursive function for finding matrix multiplication costs and discuss its efficiency compared to the standard dynamic programming approach.

💡 Hint: Think about how overlapping subproblems can reduce repeated calculations.

Challenge and get performance evaluation