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Multiplying a Vector by a Matrix

Answer Keys Here

Aligned To Common Core Standard:

High School - HSN-VM.C.11

How to Multiply a Vector by a Matrix? Multiplication between a matrix and a vector is very common. In order to learn about how multiplication between a matrix A and a vector X, also known as matrix-vector product, all we need to do is view vector X as a column matrix. Therefore, if A is a vector m x n matrix (i.e., multiplied with n columns), the product Ax is defined by n x 1. If we let A x = b, then b is m x 1 column-vector. To put it simply, the number of rows in A determines the number of rows in product b. It may confuse you in the first look, but the process is quite simple. It only takes the dot product of x to be multiplied with each of the row of A. This is the reason the number of columns in A has to be equal the number of elements/components in vector x. These worksheets will help you understand how to find the products of a vector and a matrix. The lessons show you how step by step.

Printable Worksheets And Lessons

Homework Sheets

This is where I usually have students draw lines to show how to process the product of the values.

  • Homework 1 - The first matrix (c) has 3 rows. The second matrix (x) has 1 column. So the product will have 3 rows and 1 column (3 x 1).
  • Homework 2 - You need to figure out the number of rows and columns the product will have. This is determined by the number of rows of the first matrix.
  • Homework 3 - We have many three by ones here.

Practice Worksheets

These are orientated slight differently than the homework. I have seen this format on several different assessments.

  • Practice 1 - Find the matrix product of C and vector x.
  • Practice 2 - Find the product of the vector and the matrix.
  • Practice 3 - This is a technique and calculation that computers process quicker than you could read them.

Math Skill Quizzes

Test out your skills on this topic.

  • Quiz 1 - The key is understand every element in both the vector and matrix.
  • Quiz 2 - This introduces you to the vector outer product technique.
  • Quiz 3 - I would spend a good amount of time pushing in on these.