3.4-04 Multiplication by columns and rows

Multiplication by columns and rows — linear algebra practice

Reinterpret multiplication as transforming columns of the right factor or combining rows of that factor. Practice selected columns, diagonal scaling, zero-column consequences and situations where known actions avoid reconstructing an entire matrix. These viewpoints complement the entrywise formula.

What you will practise

• Build products from column images
• Use row combinations
• Distinguish left row scaling from right column scaling

This microlearning belongs to Module 3 of the Complete Linear Algebra Course. Single-select and multiselect questions progress from interpretation to calculation, application and error diagnosis. Each problem is self-contained, and the explanations show how to justify a result rather than only identify a choice. In multiselect tasks, assess each statement separately; the number of correct choices varies.

Before starting, review standard matrix columns and multiplication. Work through the reasoning on paper, compare your method with the explanation and revisit the assumptions behind any missed item. These skills prepare you to choose a useful representation for a product.