21. Linear Algebra

Try these first

1. 1.

   Define what a system of linear equations is.

   Hint

   Think about how different equations can intersect.

2. 2.

   What is an identity matrix?

   Hint

   What happens when you multiply any matrix by it?

3. 3.

   What is a system of linear equations?

   • Multiple equations with distinct variables
   • A single equation involving multiple variables
   • A set of equations involving the same variables

   Hint

   Think about how equations can relate to each other.

4. 4.

   True or False: Eigenvalues can be zero.

   • True
   • False

   Hint

   What does zero mean for a transformation?

5. 5.

   Consider the matrix A = [[4, 2], [1, 3]]. Determine if A is singular or non-singular.

   Hint

   Focus on the determinant calculation!

6. 6.

   A system of equations is given: x + y + z = 6, 2x - y + 3z = 14, and -x + 4y - z = -2. Determine the values of x, y, and z.

   Hint

   Try substituting back into one of the original equations for checking.