Consider the matrix a. a = 1 0 1 1 0 0 0 0 0 find the characteristic polynomial for the matrix a. (write your answer in terms of λ.) (1−λ)λ2 find the real eigenvalues for the matrix a. (enter your answers as a comma-separated list.) λ = 1, 0 find a basis for each eigenspace for the matrix a. (small

Answer with Step-by-step explanation:

We are given that a matrix

a.We have to find characteristic polynomial in terms of A

We know that characteristic equation of given matrix

Where I is identity matrix of the order of given matrix

I=

Substitute the values then, we get

Hence, characteristic polynomial =

b.We have to find the eigen value  for given matrix

Then , we get

Hence, real eigen values of for the matrix are 0,0 and 1.

c.Eigen space corresponding to eigen value 1 is the null space of matrix

Apply

Now,(A-I)x=0[/tex]

Substitute the values then we get

Then , we get

And

Null space N(A-I) consist of vectors

x=

For any scalar

Hence, the basis of eigen vector corresponding to eigen value 1 is given by

Eigen space corresponding to 0 eigen value

Then,

Substitute

Then, we get

Therefore, the null space consist of vectors

Therefore, the basis of eigen space corresponding to eigen value 0 is given by

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

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