Matrix Meaning
Why do this problem?
This problem asks students to consider the geometrical properties of matrix transformations in order to gain a greater understanding of matrix algebra, in 2 and 3 dimensions.
Possible approach
The problem works well as a discussion activity. Students could work with a partner and consider each statement first in 2D and then in 3D. After allowing them some time to consider the statements, work with examples, and think about the geometrical interpretation of the situation, bring the class together to discuss their ideas.
Encourage justifications which use geometrical reasoning as well as those using algebra. If a statement is sometimes true, it is important for students to identify when it is true, and geometrically speaking, why there are situations where it is and isn't true.
Encourage the use of sketches to show counterexamples!
Key questions
Possible extension
Possible support
There are more matrix problems in this feature.
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