[ eigenvalues and eigenvectors] Prove that (v1, v2, v3) is a basis of R^3
Given a 3 x 3 matrix A with 3 distinct eigenvalues λ1, λ2, λ3, with its respective eigenvectors v1, v2, v2. Prove that (v1, v2, v3) is a basis of R^3
Answer
Answers can be viewed only if
- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.
- answered
- 125 views
- $4.00
Related Questions
- Linear algebra| finding a base
- Prove that $V={(𝑥_1,𝑥_2,⋯,𝑥_n) \in ℝ^n ∣ 𝑥_1+𝑥_2+...+𝑥_{𝑛−1}−2𝑥_𝑛=0}\}$ is a subspace of $\R^n$.
- Linear Algebra - Vectors and Linear Systems
- Consider the vector v = (3, 4, 5)^T, calculate the orthogonal projection
- Find eigenvalues and eigenvectors of $\begin{pmatrix} 1 & 6 & 0 \\ 0& 2 & 1 \\ 0 & 1 & 2 \end{pmatrix} $
- Does $\sum_{n=2}^{\infty}\frac{\sin n}{n \ln n}$ converge or diverge?
- Relating dot product divided with square of the vector while changing basis of vector
- Show that eigenvectors of a symmetric matrix are orthogonal