21.4.1. Definition

Try these first

1. 1.

   What is the definition of a matrix inverse?

   Hint

   Focus on what it means for matrices to multiply to the identity.

2. 2.

   Why can't a singular matrix have an inverse?

   Hint

   Think about the properties of determinants.

3. 3.

   What is the condition for a matrix to have an inverse?

   • It must be singular
   • It must be non-singular
   • It must be a scalar

   Hint

   Remember the definition of non-singular.

4. 4.

   True or False: The identity matrix has an inverse.

   • True
   • False

   Hint

   Think about the nature of identity.

5. 5.

   Given matrix E = [[1, 1], [1, 1]], explain why it does not have an inverse and confirm the determinant's role.

   Hint

   Verify linear dependence of rows.

6. 6.

   Calculate the inverse of the following matrix F = [[4, 2], [3, 1]] using the Gauss-Jordan method. Show your calculations.

   Hint

   Use augmented form and apply row reduction step by step.