If A = [[1, 2], [3, 4]], what is the eigenvalue of A?
Practice Questions
1 question
Q1
If A = [[1, 2], [3, 4]], what is the eigenvalue of A?
5
2
3
1
The eigenvalues are found from the characteristic polynomial λ^2 - 5λ + 2 = 0, which gives λ = 5.
Questions & Step-by-step Solutions
1 item
Q
Q: If A = [[1, 2], [3, 4]], what is the eigenvalue of A?
Solution: The eigenvalues are found from the characteristic polynomial λ^2 - 5λ + 2 = 0, which gives λ = 5.
Steps: 12
Step 1: Write down the matrix A, which is [[1, 2], [3, 4]].
Step 2: To find the eigenvalues, we need to calculate the characteristic polynomial. This is done by finding the determinant of (A - λI), where I is the identity matrix and λ is a variable.
Step 3: The identity matrix I for a 2x2 matrix is [[1, 0], [0, 1]].
Step 4: Subtract λI from A: A - λI = [[1-λ, 2], [3, 4-λ]].
Step 5: Now, calculate the determinant of the matrix (A - λI): det([[1-λ, 2], [3, 4-λ]]).
Step 6: The determinant is calculated as (1-λ)(4-λ) - (2)(3).
