The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:.

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

to find the eigenvalues of the matrix you use the following:

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

and by taking the determinant:

and the roots of this polynomial is:

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

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step-by-step explanation:

b

step-by-step explanation:

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