22.5.3 - Diagonal Matrix
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Practice Questions
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Define a diagonal matrix in your own words.
💡 Hint: Consider where the non-zero elements can be located.
If a diagonal matrix has three non-zero elements, what is its rank?
💡 Hint: Remember, rank is about counting non-zero diagonal elements.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the rank of the diagonal matrix D = [[3, 0, 0], [0, 4, 0], [0, 0, 0]]?
💡 Hint: Count the non-zero elements on the diagonal.
True or False: A zero matrix is considered a diagonal matrix.
💡 Hint: Reflect on the definition of diagonal matrices.
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Challenge Problems
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Given the diagonal matrix D = [[7, 0, 0], [0, 5, 0], [0, 0, -3]], calculate the rank and explain your method.
💡 Hint: Refer to how many diagonal entries you see that are non-zero.
If you manipulate a diagonal matrix by setting one of its non-zero diagonal entries to zero, how would that change its rank? Provide an example.
💡 Hint: Think about how rank is determined by counting non-zeros.
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