MATH-12 · Undergraduate · ENGLISH · PLANNED
Build the picture, explain the rule, work an example, then justify it.
Study time is an initial activity estimate, excluding extra reading, revision and extended laboratory or project work. Videos and question bodies have not been produced by adding this outline.
Complete these courses or demonstrate equivalent knowledge. These are recommended prerequisites, not enforced enrolment locks.
YouTube playlist: ARK Mathematics | Linear Algebra I: Matrices and Systems
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Sign in to save this learning pathPractical outcome: Represent shop stock by product and branch.
Explain what is a matrix using a visual and one worked real-world example. Context: Represent shop stock by product and branch. End with a prediction or check-for-understanding.
Explain rows columns and dimensions using a visual and one worked real-world example. Context: Represent shop stock by product and branch. End with a prediction or check-for-understanding.
Explain reading a matrix entry using a visual and one worked real-world example. Context: Represent shop stock by product and branch. End with a prediction or check-for-understanding.
Explain matrix equality using a visual and one worked real-world example. Context: Represent shop stock by product and branch. End with a prediction or check-for-understanding.
Explain matrix addition using a visual and one worked real-world example. Context: Represent shop stock by product and branch. End with a prediction or check-for-understanding.
Use the first concepts from this section. Represent shop stock by product and branch. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain matrix subtraction using a visual and one worked real-world example. Context: Represent shop stock by product and branch. End with a prediction or check-for-understanding.
Explain scalar multiplication using a visual and one worked real-world example. Context: Represent shop stock by product and branch. End with a prediction or check-for-understanding.
Explain matrix multiplication using a visual and one worked real-world example. Context: Represent shop stock by product and branch. End with a prediction or check-for-understanding.
Explain why multiplication order matters using a visual and one worked real-world example. Context: Represent shop stock by product and branch. End with a prediction or check-for-understanding.
Explain transpose using a visual and one worked real-world example. Context: Represent shop stock by product and branch. End with a prediction or check-for-understanding.
Represent shop stock by product and branch. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering What is a matrix, Rows columns and dimensions, Reading a matrix entry and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Solve a small production-planning system and verify it.
Explain augmented matrices using a visual and one worked real-world example. Context: Solve a small production-planning system and verify it. End with a prediction or check-for-understanding.
Explain elementary row operations using a visual and one worked real-world example. Context: Solve a small production-planning system and verify it. End with a prediction or check-for-understanding.
Explain row echelon form using a visual and one worked real-world example. Context: Solve a small production-planning system and verify it. End with a prediction or check-for-understanding.
Explain reduced row echelon form using a visual and one worked real-world example. Context: Solve a small production-planning system and verify it. End with a prediction or check-for-understanding.
Explain pivot variables using a visual and one worked real-world example. Context: Solve a small production-planning system and verify it. End with a prediction or check-for-understanding.
Use the first concepts from this section. Solve a small production-planning system and verify it. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain free variables using a visual and one worked real-world example. Context: Solve a small production-planning system and verify it. End with a prediction or check-for-understanding.
Explain consistent systems using a visual and one worked real-world example. Context: Solve a small production-planning system and verify it. End with a prediction or check-for-understanding.
Explain matrix inverses using a visual and one worked real-world example. Context: Solve a small production-planning system and verify it. End with a prediction or check-for-understanding.
Explain singular matrices using a visual and one worked real-world example. Context: Solve a small production-planning system and verify it. End with a prediction or check-for-understanding.
Explain lu factorisation using a visual and one worked real-world example. Context: Solve a small production-planning system and verify it. End with a prediction or check-for-understanding.
Solve a small production-planning system and verify it. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Augmented matrices, Elementary row operations, Row echelon form and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Use a transformation to rotate a simple image.
Explain vectors as displacements using a visual and one worked real-world example. Context: Use a transformation to rotate a simple image. End with a prediction or check-for-understanding.
Explain vector addition using a visual and one worked real-world example. Context: Use a transformation to rotate a simple image. End with a prediction or check-for-understanding.
Explain dot product using a visual and one worked real-world example. Context: Use a transformation to rotate a simple image. End with a prediction or check-for-understanding.
Explain span using a visual and one worked real-world example. Context: Use a transformation to rotate a simple image. End with a prediction or check-for-understanding.
Explain linear independence using a visual and one worked real-world example. Context: Use a transformation to rotate a simple image. End with a prediction or check-for-understanding.
Use the first concepts from this section. Use a transformation to rotate a simple image. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain basis using a visual and one worked real-world example. Context: Use a transformation to rotate a simple image. End with a prediction or check-for-understanding.
Explain dimension using a visual and one worked real-world example. Context: Use a transformation to rotate a simple image. End with a prediction or check-for-understanding.
Explain rank using a visual and one worked real-world example. Context: Use a transformation to rotate a simple image. End with a prediction or check-for-understanding.
Explain null space using a visual and one worked real-world example. Context: Use a transformation to rotate a simple image. End with a prediction or check-for-understanding.
Explain linear transformations using a visual and one worked real-world example. Context: Use a transformation to rotate a simple image. End with a prediction or check-for-understanding.
Use a transformation to rotate a simple image. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Vectors as displacements, Vector addition, Dot product and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Combine all three sections: Use a transformation to rotate a simple image. Submit an original worked artifact, evidence or tests, assumptions and a reflection. Rubric: correctness, method, practical usefulness, reproducibility and communication. Self-reviewed, not certified.
6–12 balanced questions sampling every section of Linear Algebra I: Matrices and Systems, including interpretation, calculation or reasoning, a misconception and a new application. Passing is 70%; review errors before retrying.
Visual constructions, worked problems and proofs. Guided work leads to an independent attempt, with a diagram, explanation, trace, calculation or tested artifact. Question bodies are generated when opened in your private learning path. Programming submissions are stored as text; the platform does not execute submitted code.
Use original or appropriately licensed datasets. Practical science activities use models or supplied data unless a qualified supervisor has reviewed a physical experiment.
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