Practice Upper Or Lower Triangular Matrix (22.5.4) - Rank of a Matrix - Mathematics (Civil Engineering -1)

Practice: Upper or Lower Triangular Matrix

Lesson 22.5.4Rank of a Matrix

Practise this section

8 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Identify the following matrix as upper or lower triangular: $\begin{pmatrix} 1 & 3 & 5 \\ 0 & 2 & 4 \\ 0 & 0 & 0 \end{pmatrix}$
Show hintHide hint
Look where the non-zero elements are located.
Question 2.
What is the rank of the following matrix? $\begin{pmatrix} 1 & 2 & 0 \\ 0 & 0 & 0 \\ 0 & 3 & 1 \end{pmatrix}$
Show hintHide hint
Count the number of non-zero rows.
3Question 3.
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.
Show hintHide hint
Think about where the non-zero elements are in the matrix.
4Question 4.
The rank of a triangular matrix is equal to the number of non-zero rows.
- True
- False
Show hintHide hint
Recall the definition of rank in the context of triangular matrices.
Question 5.
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?
Show hintHide hint
Count the rows that contain non-zero elements.
Question 6.
Construct a lower triangular matrix of order 4 with a rank of 3 and show your work.
Show hintHide hint
Ensure there are three non-zero rows in your matrix.

4 more questions in this section. Enroll free to practise them all.