Practice Upper or Lower Triangular Matrix - 22.5.4 | 22. Rank of a Matrix | Mathematics (Civil Engineering -1)
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22.5.4 - Upper or Lower Triangular Matrix

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

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.

Question 2

Easy

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.

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

What defines an upper triangular matrix?

  • A matrix with all zeroes above the diagonal.
  • A matrix with all zeroes below the diagonal.
  • A matrix with non-zero elements in the first column.

💡 Hint: Think about where the non-zero elements are in the matrix.

Question 2

The rank of a triangular matrix is equal to the number of non-zero rows.

  • True
  • False

💡 Hint: Recall the definition of rank in the context of triangular matrices.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation