The number of distinct eigenvalues of the matrix A = ≤ft[ {*20c 2&2&3&3\\ 0&1&1&1\\ {*20c 0\\ 0 }&{*20c 0\\ 0 }&{*20c 3\\ 0 }&{*20c 3\\ 2 } } ] is equal to ______.
Correct Answer
Solution & Step-by-step Explanation
In the range: 3 - 3
A = ≤ft[ {*20c 2&2&3&3\\ 0&1&1&1\\ {*20c 0\\ 0 }&{*20c 0\\ 0 }&{*20c 3\\ 0 }&{*20c 3\\ 2 } } ]
The given matrix is a upper triangular matrix
For upper triangular matrix, eigen values are the diagonal elements
Hence,
λ₁ = 2 = λ₄
λ₂ = 1
λ₃ = 3
Hence, there are three distinct eigen values.
A = ≤ft[ {*20c 2&2&3&3\\ 0&1&1&1\\ {*20c 0\\ 0 }&{*20c 0\\ 0 }&{*20c 3\\ 0 }&{*20c 3\\ 2 } } ]
The given matrix is a upper triangular matrix
For upper triangular matrix, eigen values are the diagonal elements
Hence,
λ₁ = 2 = λ₄
λ₂ = 1
λ₃ = 3
Hence, there are three distinct eigen values.