Consider the tridiagonal matrix
![1521_Tridiagonal Matrix.png](https://secure.tutorsglobe.com/CMSImages/1521_Tridiagonal Matrix.png)
1. Why do we know that Naive Gaussian Elimination will work to solve the system of equations Ax→ = b→ where
![2145_Matrix.png](https://secure.tutorsglobe.com/CMSImages/2145_Matrix.png)
for any
?
2. Solve the system of equations Ax→ = b→ where
![1944_Matrix2.png](https://secure.tutorsglobe.com/CMSImages/1944_Matrix2.png)
using Naive Gaussian elimination
3. How do we know that the eigenvalues of A are all real and distinct before we calculate them?
4. Find the characteristic polynomial of A.
5. Find the eigenvalues of A. Hint: The characteristic polynomial can be easily factored into the product of two linear terms and a quadratic that you use the quadratic formula on.