21.4.2. Conditions

Try these first

1. 1.

   Define what it means for a matrix to be non-singular.

   Hint

   Think about how the determinant relates to the matrix's invertibility.

2. 2.

   What is the relationship between a matrix and its inverse?

   Hint

   Consider what happens when you multiply the inverse with the original matrix.

3. 3.

   What must be true for a matrix to have an inverse?

   • It must be singular
   • It must have a determinant of zero
   • It must be non-singular

   Hint

   Recall the definition of singular matrices.

4. 4.

   True or False: A singular matrix cannot have an inverse.

   • True
   • False

   Hint

   Think about how determinants affect inversibility.

5. 5.

   Determine if the following matrix is invertible: A = [[4, 2], [2, 1]]. Justify your answer with calculations.

   Hint

   Calculate the determinant!

6. 6.

   If B = [[1, 3], [3, 7]], what can you say about its inverse and detail how you would find it?

   Hint

   Recall how to calculate the determinant and apply the inverse formula.