No of linearly independant (distinct) eigen vectors = No of distinct eigrn values.
Here, as it is an upper triangular matrix, eigen values are 2,2. Distinct value = 2
Thus. only 1 vector. Hence, option (B).
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Btw, lot of people are confused between linearly independent eigen vectors, linearly independent solutions and linearly independent Rows or Columns. Here is a quick solution to solve such problems....
**Linearly Independent ............
1) Eigen Vectors : No. of distinct Eigen values
2) Solutions : N-R (i.e, Variables - Rank)
3) Rows or Columns : R
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There are many questions in the past for all 3 types mentioned above. Do practice it well :)