Question

The matrix \begin{equation} A = \begin{bmatrix} 0 & 0 & 0\\ -3 & 3 & 0\\ 3 & -3 & 0 \end{bmatrix} \end{equation} has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace. The eigenvalue $\lambda_1$ is and a basis for its associated eigenspace is The eigenvalue $\lambda_2$ is and a basis for its associated eigenspace is

          The matrix
\begin{equation*}
A = \begin{bmatrix} 0 & 0 & 0\\ -3 & 3 & 0\\ 3 & -3 & 0 \end{bmatrix}
\end{equation*}
has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace.
The eigenvalue $\lambda_1$ is  and a basis for its associated eigenspace is
The eigenvalue $\lambda_2$ is  and a basis for its associated eigenspace is

The matrix

A =
< b m a t r i x >

has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace.
The eigenvalue λ1 is and a basis for its associated eigenspace is
The eigenvalue λ2 is and a basis for its associated eigenspace is

Added by David Y.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Adi S

11/07/2023

Step 1

The characteristic equation is: \[ \det \begin{bmatrix} -\lambda & 3 \\ 3 & -3-\lambda \end{bmatrix} = 0 \] Expanding the determinant, we get: \[ (-\lambda)(-3-\lambda) - 3(3) = 0 \] \[ \lambda^2 + 3\lambda - 9 = 0 \] Using the quadratic formula, we find the Show more…

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The matrix [ egin{bmatrix} 0 & 3 \ 3 & -3 end{bmatrix} ] has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace. The eigenvalue is and a basis for its associated eigenspace. The eigenvalue is and a basis for its associated eigenspace. Note: You can earn partial credit on this problem. Preview My Answer Submit Answer