Multiplying a matrix by a vector

The  exercise appears under the Precalculus Math Mission. This exercise multiplies matrices against vectors.

Types of Problems
There is one type of problem in this exercise:


 * 1) Multiply the matrix against the vector: This problem provides a matrix and a vector that are supposed to be multiplied together. The student is expected to find the correct product and write the entries in the blank 3x3 matrix.Mambav1.png

Strategies
Knowledge of the mechanics behind matrix multiplication is encouraged to ensure success on this exercise.
 * 1) To find the a_mn entry of a product one needs to find the dot product of the mth row of the first matrix and the nth column of the second matrix.
 * 2) Since the vector has only one column, the result of the product will also be a vector, that is, it will only be a single column. The number of entries will be the number of rows of the first matrix.

Real-life Applications

 * 1) Matrices are the foundational concept in linear algebra.
 * 2) Matrices can be a method for efficiently solving systems of linear equations.