MAT3700
Assignment 03
Due 15 August 2025
, Eigenvalues and Gaussian Elimination Linear Algebra Solutions
Solutions to Linear Algebra Problems
Eigenvalues, Eigenvectors, and Gaussian Elimination
Question 1
3 6
1. Eigenvalues of B =
1 4
Step 1: Compute B − λI
3−λ 6
B − λI =
1 4−λ
Step 2: Compute the determinant
det(B − λI) = (3 − λ)(4 − λ) − 6 = λ2 − 7λ + 6
Step 3: Solve the characteristic equation
λ2 − 7λ + 6 = 0 ⇒ (λ − 1)(λ − 6) = 0 ⇒ λ = 1, 6
Answer: λ = 1, 6
1
Assignment 03
Due 15 August 2025
, Eigenvalues and Gaussian Elimination Linear Algebra Solutions
Solutions to Linear Algebra Problems
Eigenvalues, Eigenvectors, and Gaussian Elimination
Question 1
3 6
1. Eigenvalues of B =
1 4
Step 1: Compute B − λI
3−λ 6
B − λI =
1 4−λ
Step 2: Compute the determinant
det(B − λI) = (3 − λ)(4 − λ) − 6 = λ2 − 7λ + 6
Step 3: Solve the characteristic equation
λ2 − 7λ + 6 = 0 ⇒ (λ − 1)(λ − 6) = 0 ⇒ λ = 1, 6
Answer: λ = 1, 6
1
