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AI & ML · Linear Algebra

Rank & linear independence

513 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.

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

  1. Warm-up

    Find the rank and the nullity of the diagonal matrix D=(−200010001)D = \begin{pmatrix} -2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}.

  2. Warm-up

    Find the rank and the nullity of the diagonal matrix D=(−2000−10001)D = \begin{pmatrix} -2 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{pmatrix}.

  3. Warm-up

    Find the rank and the nullity of the diagonal matrix D=(000020001)D = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 1 \end{pmatrix}.

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