CCSS.Math.Content.HSN-VM.C.11
The standard
(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
Common Core State Standards for Mathematics · Vector and Matrix Quantities
What this standard means
Students need to treat a vector as a column matrix and multiply it by a compatible matrix. They should track dimensions, compute each entry, and understand the result as a new vector, not just a list of numbers.
Mastery looks like students explaining how a matrix changes a vector, such as stretching, reflecting, rotating, or shearing it. They can connect the arithmetic to movement on a coordinate plane. Common trouble spots are multiplying in the wrong order, mixing up rows and columns, and doing calculations without checking whether the dimensions match.
Ways to teach it
- Have students plot a triangle, apply a given 2 by 2 matrix to each vertex, then graph the transformed image on grid paper.
- Ask students to write what the matrix [[1,0],[0,-1]] does to three different vectors and explain the pattern.
- Give one matrix and four vectors, then ask students to compute one image vector and identify one impossible product.
- Show how a phone photo resize or flip can be modeled by applying a transformation matrix to points on the image.
Plan a lesson for CCSS.Math.Content.HSN-VM.C.11
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Related standards
- CCSS.Math.Content.HSN-VM.C.7
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
- CCSS.Math.Content.HSN-VM.C.8
(+) Add, subtract, and multiply matrices of appropriate dimensions.
- CCSS.Math.Content.HSN-VM.C.12
(+) Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
- CCSS.Math.Content.HSN-VM.B.5
(+) Multiply a vector by a scalar.