AI & ML · Linear Algebra

Eigenvalues & eigenvectors

304 problems in this skill, each with a solver-verified answer key. Answers are checked the moment you submit — with a hint if you want one and a worked solution afterwards.

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Warm-up
A $2 \times 2$ matrix $A$ has eigenvalues $\lambda_1 = -3$ and $\lambda_2 = 3$ . Find (i) the trace of $A$ and (ii) the determinant of $A$ .
Warm-up
A $2 \times 2$ matrix $A$ has eigenvalues $\lambda_1 = 2$ and $\lambda_2 = -4$ . Find (i) the trace of $A$ and (ii) the determinant of $A$ .
Warm-up
A $2 \times 2$ matrix $A$ has eigenvalues $\lambda_1 = -1$ and $\lambda_2 = 3$ . Find (i) the trace of $A$ and (ii) the determinant of $A$ .

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