Question

(1 point) If \(\vec{v}_1 = \begin{bmatrix} 4 \\ 5 \end{bmatrix}\) and \(\vec{v}_2 = \begin{bmatrix} -4 \\ 0 \end{bmatrix}\) are eigenvectors of a matrix A corresponding to the eigenvalues \(\lambda_1 = 4\) and \(\lambda_2 = 3\), respectively, then \(A(\vec{v}_1 + \vec{v}_2) = \begin{bmatrix} \\\\ \end{bmatrix}\) and \(A(-3\vec{v}_1) = \begin{bmatrix} \\\\ \end{bmatrix}\)

          (1 point) If \(\vec{v}_1 = \begin{bmatrix} 4 \\ 5 \end{bmatrix}\) and \(\vec{v}_2 = \begin{bmatrix} -4 \\ 0 \end{bmatrix}\) are eigenvectors of a matrix A corresponding to the eigenvalues \(\lambda_1 = 4\) and \(\lambda_2 = 3\), respectively,
then \(A(\vec{v}_1 + \vec{v}_2) = \begin{bmatrix} \\\\ \end{bmatrix}\)
and \(A(-3\vec{v}_1) = \begin{bmatrix} \\\\ \end{bmatrix}\)

(1 point) If v⃗1 =
< b m a t r i x > and v⃗2 =
< b m a t r i x > are eigenvectors of a matrix A corresponding to the eigenvalues λ1 = 4 and λ2 = 3, respectively,
then A(v⃗1 + v⃗2) =
< b m a t r i x >
and A(-3v⃗1) =
< b m a t r i x >

Added by Jennifer M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

05/17/2023

Step 1

vec(v)_(1) + vec(v)_(2) = [[4],[5]] + [[-4],[0]] = [[4-4],[5+0]] = [[0],[5]] Show more…

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Thanks for your feedback!

(1 point) If vec(v)_(1)=[[4],[5]] and vec(v)_(2)=[[-4],[0]] are eigenvectors of a matrix A corresponding to the eigenvalues lambda _(1)=4 and lambda _(2)=3, respectively, then A(vec(v)_(1)+vec(v)_(2))=[◻] and (1 point) If 1 and2 are eigenvectors of a matrix A corresponding to the eigenvalues X = 4 and X =3, respectively thenA(+) andA(-3)