21.4. Inverse of a Matrix

Try these first

1. 1.

   Define the term 'matrix inverse.'

   Hint

   Think about how two matrices interact when multiplied.

2. 2.

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

   Hint

   Recall what the determinant indicates about the matrix.

3. 3.

   What is the main property of the matrix inverse?

   • AA⁻¹ = I
   • A + A⁻¹ = I
   • A⁻¹ A = 0

   Hint

   Look for equations that yield the identity matrix.

4. 4.

   True or False: A singular matrix has an inverse.

   • True
   • False

   Hint

   Reflect on determinant properties.

5. 5.

   Given the following matrix, find the inverse using the adjoint method: A = [[4, 7], [2, 6]].

   Hint

   Remember the formula involving determinant and adjoint.

6. 6.

   Use the Gauss-Jordan method to find the inverse of the matrix B = [[3, 2], [1, 1]]. Show the step-by-step transformation.

   Hint

   Focus on making the left side the identity matrix.