21.1.1. Definition

Try these first

1. 1.

   What is a system of linear equations?

   Hint

   Think about how multiple equations can relate to each other.

2. 2.

   Define a coefficient matrix.

   Hint

   What do you call the numbers in front of the variables?

3. 3.

   What is the definition of a system of linear equations?

   • A group of nonlinear equations
   • A set of equations with the same variables
   • An equation with one variable

   Hint

   Remember the definition discussed in class.

4. 4.

   True or False: A consistent system of equations always has exactly one solution.

   • True
   • False

   Hint

   Think about what it means to be consistent.

5. 5.

   A system of three equations is given. Identify its consistency: 2x + 3y + z = 6, x - y + 2z = 3, 4x + 6y + 2z = 12. Is it consistent or inconsistent?

   Hint

   Think about how one equation can be derived from another; this implies dependence.

6. 6.

   Construct a matrix for the system defined by: 'The sum of two numbers is 10, and their difference is 2.' Solve for the two numbers using matrix methods.

   Hint

   Matrix methods, like elimination, might help simplify solving the equations.