Question

The matrix A = egin{bmatrix} 1 & 0 & 0 \ -4 & 1 & 0 \ 2 & 0 & 1 end{bmatrix} has one real eigenvalue. Find this eigenvalue and a basis of the eigenspace. The eigenvalue is A basis for the eigenspace is left{ egin{bmatrix} phantom{x} \ phantom{x} \ phantom{x} end{bmatrix}, egin{bmatrix} phantom{x} \ phantom{x} \ phantom{x} end{bmatrix} ight}. Note: You can earn partial credit on this problem.

          The matrix
A = egin{bmatrix} 1 & 0 & 0 \ -4 & 1 & 0 \ 2 & 0 & 1 end{bmatrix}
has one real eigenvalue. Find this eigenvalue and a basis of the eigenspace.
The eigenvalue is
A basis for the eigenspace is left{ egin{bmatrix} phantom{x} \ phantom{x} \ phantom{x} end{bmatrix}, egin{bmatrix} phantom{x} \ phantom{x} \ phantom{x} end{bmatrix} 
ight}.
Note: You can earn partial credit on this problem.

The matrix
A = eginbmatrix 1 0 0 -4 1 0 2 0 1 endbmatrix
has one real eigenvalue. Find this eigenvalue and a basis of the eigenspace.
The eigenvalue is
A basis for the eigenspace is left eginbmatrix phantomx phantomx phantomx endbmatrix, eginbmatrix phantomx phantomx phantomx endbmatrix
ight.
Note: You can earn partial credit on this problem.

Added by Gregory M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/07/2023

Step 1

To do this, we need to solve the characteristic equation det(A - λI) = 0, where I is the identity matrix and λ is the eigenvalue we are looking for. det(A - λI) = det([1-λ 2 3; 4 5-λ 6; 7 8 9-λ]) = (1-λ)[(5-λ)(9-λ)-6(8)] - 2[(4)(9-λ)-6(7)] + 3[(4)(8)-(5-λ)(7)] = Show more…

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The matrix A = has one real eigenvalue. Find this eigenvalue and a basis of the eigenspace. The eigenvalue is A basis for the eigenspace is Note: You can earn partial credit on this problem.