10 levels · 20 original questions

Linear algebra practice

Build intuition for vectors, matrices and spaces in 10 short levels. Choose an answer, read the explanation, and continue at your own pace.

View levels · Open learning diagnosis

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Level 1 of 10

Length and direction

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Learning signals

Only 20 questions, two per topic. These provisional signals are not a complete ability assessment; understanding needs new questions and later review.

Length and direction: Insufficient evidence
Fewer than two different questions have been answered. Repeating one does not increase coverage.
0/2 questions observed; 0/2 correct on first try without recorded help; 0 first answers with help or unknown prior exposure; 0 retries; 0 incorrect answers.
0 questions correct with help, on retry or with unknown prior exposure (not independent first answers).
Review the notes ·
Add and scale: Insufficient evidence
Fewer than two different questions have been answered. Repeating one does not increase coverage.
0/2 questions observed; 0/2 correct on first try without recorded help; 0 first answers with help or unknown prior exposure; 0 retries; 0 incorrect answers.
0 questions correct with help, on retry or with unknown prior exposure (not independent first answers).
Review the notes ·
Build a linear combination: Insufficient evidence
Fewer than two different questions have been answered. Repeating one does not increase coverage.
0/2 questions observed; 0/2 correct on first try without recorded help; 0 first answers with help or unknown prior exposure; 0 retries; 0 incorrect answers.
0 questions correct with help, on retry or with unknown prior exposure (not independent first answers).
Review the notes ·
What can the vectors span?: Insufficient evidence
Fewer than two different questions have been answered. Repeating one does not increase coverage.
0/2 questions observed; 0/2 correct on first try without recorded help; 0 first answers with help or unknown prior exposure; 0 retries; 0 incorrect answers.
0 questions correct with help, on retry or with unknown prior exposure (not independent first answers).
Review the notes ·
Spot dependence: Insufficient evidence
Fewer than two different questions have been answered. Repeating one does not increase coverage.
0/2 questions observed; 0/2 correct on first try without recorded help; 0 first answers with help or unknown prior exposure; 0 retries; 0 incorrect answers.
0 questions correct with help, on retry or with unknown prior exposure (not independent first answers).
Review the notes ·
Read a matrix by columns: Insufficient evidence
Fewer than two different questions have been answered. Repeating one does not increase coverage.
0/2 questions observed; 0/2 correct on first try without recorded help; 0 first answers with help or unknown prior exposure; 0 retries; 0 incorrect answers.
0 questions correct with help, on retry or with unknown prior exposure (not independent first answers).
Review the notes ·
Multiply matrices: Insufficient evidence
Fewer than two different questions have been answered. Repeating one does not increase coverage.
0/2 questions observed; 0/2 correct on first try without recorded help; 0 first answers with help or unknown prior exposure; 0 retries; 0 incorrect answers.
0 questions correct with help, on retry or with unknown prior exposure (not independent first answers).
Review the notes ·
Simplify equations by rows: Insufficient evidence
Fewer than two different questions have been answered. Repeating one does not increase coverage.
0/2 questions observed; 0/2 correct on first try without recorded help; 0 first answers with help or unknown prior exposure; 0 retries; 0 incorrect answers.
0 questions correct with help, on retry or with unknown prior exposure (not independent first answers).
Review the notes ·
Inputs that become zero: Insufficient evidence
Fewer than two different questions have been answered. Repeating one does not increase coverage.
0/2 questions observed; 0/2 correct on first try without recorded help; 0 first answers with help or unknown prior exposure; 0 retries; 0 incorrect answers.
0 questions correct with help, on retry or with unknown prior exposure (not independent first answers).
Review the notes ·
Reachable outputs and rank: Insufficient evidence
Fewer than two different questions have been answered. Repeating one does not increase coverage.
0/2 questions observed; 0/2 correct on first try without recorded help; 0 first answers with help or unknown prior exposure; 0 retries; 0 incorrect answers.
0 questions correct with help, on retry or with unknown prior exposure (not independent first answers).
Review the notes ·