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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students check that the matrix has one column for each vector entry. They use each matrix row to calculate one entry of the output vector. They connect the result to a change such as rotation, reflection, scaling, or shear.
What Mastery Looks Like
- A student writes vectors as columns, confirms dimensions, and computes each row's dot product accurately. They predict the output dimension and graph the input and output vectors. They explain the geometric change shown by the matrix.
Common Misconceptions
- Students often reverse the multiplication order or multiply matching entries instead of taking dot products. Some use matrix columns rather than rows to build output entries. Others assume every matrix only scales a vector, missing rotations, reflections, and shears.
How to Assess It
- Exit ticket: Apply the matrix with rows (0, -1) and (1, 0) to the column vector (3, 1). Show both row calculations, graph both vectors, and name the geometric effect.
Lesson moves
Ways to Teach It
On graph paper, students draw five vectors, apply the matrix with rows (1, 1) and (0, 1), then draw each image.
Prompt pairs: How do the rows of a matrix determine the coordinates of the output vector? Use one numerical example.
Use matrix and vector cards; teams earn a point for matching dimensions, calculating the image, and checking another team's result.
Transform the corner coordinates of a simple pixel-art shape with scaling and reflection matrices, then sketch the changed shape.
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Printable HSN-VM.C.11 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSN-VM.C.11, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSN-VM.B.5a
Matrix-vector multiplication uses scalar multiples of component entries and scaled column vectors to describe transformations of vectors.
- CCSS.Math.Content.HSN-VM.C.8
Matrix multiplication rules carry directly into computing matrix-vector products, which are needed before interpreting matrices as vector transformations.
- CCSS.Math.Content.HSN-VM.C.6
Representing data in matrices gives students familiarity with entries and dimensions needed before matrix vector multiplication.
What This Unlocks
Mastery here sets students up for these next.
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