MAIN DIAGONAL
Definition Of Main Diagonal
Main Diagonal of a matrix consists of the elements of a square from the upper left element proceeding to the down right element diagonally.
More About Main Diagonal
The sum of the elements of the main diagonal of a matrix is called Trace of the matrix.
Examples of Main Diagonal
The elements 1, 5, and 9 are the elements of the main diagonal of a 3 × 3 matrix.
Video Examples: Diagonal Lengths of a Parallelepiped
Solved Example on Main Diagonal
Ques: Identify the main diagonal elements of the matrix.
Choices:
A. 5, 1, - 7, 2
B. 5, 5, 8, - 2
C. 8, 6, - 7, 4
D. 4, - 2, 4
Correct Answer: A
Solution:
Step 1: Main diagonal of a matrix consists of the elements from the upper left element proceeding to the down right element diagonally.
Step 2: So, the elements 5, 1, - 7, 2 are the diagonal elements of the matrix.
Quick Summary
- The main diagonal exists only for square matrices.
- Elements are selected from the top-left to bottom-right.
- The sum of the elements on the main diagonal is called the trace of the matrix.
🍎 Teacher Insights
Use visual aids and color-coding to help students identify the main diagonal in various matrices. Emphasize that only square matrices have main diagonals.🎓 Prerequisites
- Matrix
- Square Matrix
- Matrix Elements
Check Your Knowledge
Q1: Which elements form the main diagonal of the matrix [[1, 2], [3, 4]]?
Q2: What is the trace of the matrix [[5, 0], [0, 5]]?
Frequently Asked Questions
Q: What kind of matrices have a main diagonal?
A: Only square matrices have a main diagonal.
Q: What is the significance of the main diagonal?
A: It is used in calculating the trace, determinant, and eigenvalues of a matrix.