LEADING ENTRY OF A MATRIX
Definition Of Leading Entry Of A Matrix
The Leading Entry in each row of a matrix is the first non-zero entry in that row.
More About Leading Entry of a Matrix
One of the criteria for a matrix to be in row echelon form is that all the leading entries of a non-zero row should be 1.
To be a matrix in row echelon form, the leading entry of each row should be to the right of the leading entries of the previous row.
Video Examples: Gauss Jordan Elimination - with audio
Example of Leading Entry of a Matrix
A = 
In the above matrix, the leading entry in the first row is - 5, the leading entry in the second row is - 6, and the leading entry in the third row is 8, as those are the first non-zero entries.
Solved Example on Leading Entry of a Matrix
Ques: Identify the leading entries in each row of a matrix shown below.
Choices:
A. 1
B. 1, 0, 0, and 0
C. 1, 9, 4, and 7
D. 2, 0, 3, and 0
Correct Answer: C
Solution:
Step 1: The leading entry in each row is the first non-zero entry in that row.
Step 2: Here, in the matrix, the leading entries in each row are 1, 9, 4, and 7.
Quick Summary
- The leading entry is the first non-zero element in a row.
- In row echelon form, leading entries are typically 1.
- Row echelon form requires leading entries to be to the right of leading entries in previous rows.
🍎 Teacher Insights
Emphasize the importance of leading entries in the context of row echelon form and solving systems of linear equations. Use visual examples with different types of matrices to illustrate the concept.🎓 Prerequisites
- Basic Matrix Operations
- Row Operations
- Understanding of Zero and Non-zero Values
Check Your Knowledge
Q1: What is the leading entry of the row [0, 0, 5, 2]?
Q2: In row echelon form, what should the leading entry ideally be?
Frequently Asked Questions
Q: What happens if a row is all zeros?
A: If a row contains only zeros, it does not have a leading entry.
Q: Can a leading entry be any non-zero number?
A: Yes, but in row echelon form, leading entries are often transformed to be 1.