Defined and undefined matrix operations

The  exercise appears under the Algebra II Math Mission. This exercise discovers whether certain matrix operations are defined or not.

Types of Problems
There are two types of problems in this exercise:


 * 1) Determine if the product is defined: This problem asks for the product of two matrices. The student is asked to determine if the product is defined.Daumo1.png
 * 2) Determine if the sum or difference is defined: This problem asks for the sum or difference of two matrices. The student is asked to determine if the operation is defined.Daumo2.png

Strategies
Knowledge of the various matrix operations are encouraged to ensure success on this exercise.
 * 1) Adding and subtracting matrices requires that the matrices have the exact same dimensions.
 * 2) Multiplying matrices requires that there are the same number of columns in the first matrix as rows on the second matrix.
 * 3) The ABij entry of the product matrix is the dot product of the ith row of the A matrix with the jth column of the B matrix.
 * 4) Some calculators can be used to perform operations such as multiplication on matrices.

Real-life Applications

 * 1) Matrices are intimately connected with Linear Algebra.
 * 2) Matrices can be used to represent data sets with cross relationships.
 * 3) Matrices have applications in number theory and cryptography.