Question: If A = [[2, 0], [0, 3]], what is the eigenvalue of A?
Options:
2
3
0
5
Correct Answer: 3
Solution:
The eigenvalues of A are the diagonal elements: 2 and 3.
If A = [[2, 0], [0, 3]], what is the eigenvalue of A?
Practice Questions
Q1
If A = [[2, 0], [0, 3]], what is the eigenvalue of A?
2
3
0
5
Questions & Step-by-Step Solutions
If A = [[2, 0], [0, 3]], what is the eigenvalue of A?
Step 1: Identify the matrix A, which is given as [[2, 0], [0, 3]].
Step 2: Recognize that the eigenvalues of a diagonal matrix are the values on its diagonal.
Step 3: Look at the diagonal elements of matrix A, which are 2 and 3.
Step 4: Conclude that the eigenvalues of matrix A are 2 and 3.
Eigenvalues – Eigenvalues are scalars associated with a linear transformation represented by a matrix, indicating how much the eigenvectors are stretched or compressed.
Diagonal Matrix – A diagonal matrix has non-zero elements only on its main diagonal, and its eigenvalues are simply the diagonal elements.
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