✏️ Practice Exercises

Linear Algebra

3 problems · Easy to Hard · Type your working · AI checks your steps

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How to use these exercises

Read the question → work it out step-by-step in the box → click Check My Working to get AI feedback. Use hints if stuck. Reveal the full solution only after you have tried.

01

easy

Are (1, 2) and (2, 4) linearly independent?

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Is one a scalar multiple of the other?

Your Working

02

medium

For A = [[2, 0], [0, 3]], find an eigenvector with λ = 3.

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A diagonal matrix has standard basis as eigenvectors.

Your Working

03

hard

Trace of A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]:

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Trace = sum of diagonal entries.

Your Working

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