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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

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 .

Eigen value Repeated then we should check for Corresponding Eigen vectors, but already B is Correct , So, no need to check :)
How to check if eigen values are repeated

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