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+2 votes
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Which of the following is true?

  1. The matrix $\begin{pmatrix}
    1&0 \\
    1&2
    \end{pmatrix}$ is not diagonalisable.
  2. The matrix $\begin{pmatrix}
    1&5 \\
    0&2
    \end{pmatrix}$ is diagonalisable.
  3. The matrix $\begin{pmatrix}
    1&1 \\
    0&1
    \end{pmatrix}$ is diagonalisable
  4. None of the above.
asked in Linear Algebra by Veteran (39.7k points) 253 1302 1929 | 150 views

1 Answer

+6 votes
Best answer

I'm getting option b ..according to diagonalization theorem 1st we have to find the eigen value of the given matrix  it says that if there are exactly n distinct eigenvalues in an n×n matrix then this matrix is diagonalizable...if eigen values repeated then we have to find the corresponding eigen vector..

a)here getting two eigen values 2 and 1 so according to theorem its diagonalisable but given is not diagonalizable so false.

b)its should be true because two different eigen values is 2 and 1.

c)false because eigen value repeated i.e 1,1 so false .

 

 

answered by (329 points) 1 4 8
selected by
Eigen value Repeated then we should check for Corresponding Eigen vectors, but already B is Correct , So, no need to check :)


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