braindrill

Eigenvectors

17 practice questionsLinear AlgebraStep-by-step solutions

Try a few

1

Which of these is an eigenvector of A=(10123)A = \begin{pmatrix} 1 & 0 \\ 12 & -3 \end{pmatrix} corresponding to the eigenvalue λ=1\lambda = 1?

A.(32)\begin{pmatrix} 3 \\ 2 \end{pmatrix}
B.(01)\begin{pmatrix} 0 \\ 1 \end{pmatrix}
C.(13)\begin{pmatrix} 1 \\ 3 \end{pmatrix}
D.(14)\begin{pmatrix} 1 \\ 4 \end{pmatrix}
🔒 Answer + full step-by-step solutionUnlock free →
2

Which of these is an eigenvector of A=(71058)A = \begin{pmatrix} 7 & -10 \\ 5 & -8 \end{pmatrix} corresponding to the eigenvalue λ=2\lambda = 2?

A.(13)\begin{pmatrix} 1 \\ 3 \end{pmatrix}
B.(21)\begin{pmatrix} 2 \\ 1 \end{pmatrix}
C.(32)\begin{pmatrix} 3 \\ 2 \end{pmatrix}
D.(11)\begin{pmatrix} 1 \\ 1 \end{pmatrix}
🔒 Answer + full step-by-step solutionUnlock free →
3

Which of these is an eigenvector of A=(3401)A = \begin{pmatrix} -3 & -4 \\ 0 & 1 \end{pmatrix} corresponding to the eigenvalue λ=3\lambda = -3?

A.(02)\begin{pmatrix} 0 \\ 2 \end{pmatrix}
B.(10)\begin{pmatrix} 1 \\ 0 \end{pmatrix}
C.(11)\begin{pmatrix} 1 \\ -1 \end{pmatrix}
D.(21)\begin{pmatrix} 2 \\ -1 \end{pmatrix}
🔒 Answer + full step-by-step solutionUnlock free →

Master eigenvectorsnot just preview it

All 17 questions with worked solutions, an AI tutor that explains every step, and games that make the drilling stick. Free to start.

Practice this topic free

No card needed · 10 free AI questions daily