Practice - Upper or Lower Triangular Matrix
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Practice Questions
Test your understanding with targeted questions
Identify the following matrix as upper or lower triangular: \[ \begin{pmatrix} 1 & 3 & 5 \ 0 & 2 & 4 \ 0 & 0 & 0 \end{pmatrix} \]
💡 Hint: Look where the non-zero elements are located.
What is the rank of the following matrix? \[ \begin{pmatrix} 1 & 2 & 0 \ 0 & 0 & 0 \ 0 & 3 & 1 \end{pmatrix} \]
💡 Hint: Count the number of non-zero rows.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What defines an upper triangular matrix?
💡 Hint: Think about where the non-zero elements are in the matrix.
The rank of a triangular matrix is equal to the number of non-zero rows.
💡 Hint: Recall the definition of rank in the context of triangular matrices.
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Challenge Problems
Push your limits with advanced challenges
Analyze the following upper triangular matrix: \[ \begin{pmatrix} 1 & 2 & 0 \ 0 & 1 & 3 \ 0 & 0 & 0 \end{pmatrix} \]. What is its rank and why?
💡 Hint: Count the rows that contain non-zero elements.
Construct a lower triangular matrix of order 4 with a rank of 3 and show your work.
💡 Hint: Ensure there are three non-zero rows in your matrix.
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