Engineering Mathematics – I
Unit VILinear Algebra Eigen Values and Eigen Vectorsa) Find Eigen Values and Eigen vectors of the following matrices.(i) 
(ii) 
b) Find Eigen values and corresponding eigen vector corresponding to lowest eigen value for the matrix.(i) 
(ii) 
c) Find eigen values and eigen vector corresponding to highest eigen value of the matrices.(i) 
(ii) 
d) Verify Cayley – Hamilton theorem for(i) 
and hence find A-1(ii) 
and find A-1(iii) 
and find A4e) Verify Cayley – Hamilton theorem for the matrix.
Hence simplify the expression.
f) Verify Cayley – Hamilton theorem for the matrix
and find A-1 and 
(ii) b) Find Eigen values and corresponding eigen vector corresponding to lowest eigen value for the matrix.(i) (ii) c) Find eigen values and eigen vector corresponding to highest eigen value of the matrices.(i) (ii) d) Verify Cayley – Hamilton theorem for(i) and hence find A-1(ii) and find A-1(iii) and find A4e) Verify Cayley – Hamilton theorem for the matrix. Hence simplify the expression.f) Verify Cayley – Hamilton theorem for the matrix and find A-1 and 
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