Calculate the value of K in the matrix A=((0,2),(K,-1))

tamnicufl

tamnicufl

Answered question

2022-09-24

If the matrix A = ( 0 2 K 1 ) satisfies A ( A 3 + 3 I ) = 2 I then value of K is ?

Answer & Explanation

Amiya Watkins

Amiya Watkins

Beginner2022-09-25Added 6 answers

The characteristic polynomial of that matrix is z 2 + z 2 K. This should be a divisor of z ( z 3 + 3 ) 2 = z 4 + 3 z 2. Now,
z 4 + 3 z 2 = ( z 2 z + 2 ) ( z 2 + z 1 ) .
Thus, K = 1 2

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