Determinants & Inverses (DP IB Applications & Interpretation (AI)): Revision Note

Determinants

What is a determinant?

• The determinant is a numerical value (positive or negative) calculated from the elements in a matrix and is used to find the inverse of a matrix

• You can only find the determinant of a square matrix

• The method for finding the determinant of a  matrix is given in your formula booklet: 

• You only need to be able to find the determinant of a  matrix by hand

  • For larger  matrices you are expected to use your GDC

• The determinant of an identity matrix is 

• The determinant of a zero matrix is 

• When finding the determinant of a multiple of a matrix or the product of two matrices:

  • (for a  matrix)

  • 

Inverse Matrices

How do I find the inverse of a matrix?

• The determinant can be used to find out if a matrix is invertible or not:

  • If , then  is invertible

  • If , then  is singular and does not have an inverse

• The method for finding the inverse of a  matrix is given in your formula booklet:

• You only need to be able to find the inverse of a  matrix by hand

  • For larger  matrices you are expected to use your GDC

• The inverse of a square matrix is the matrix  such that the product of these matrices is an identity matrix, 

  • As a result of this property:

    •  (pre-multiplying by )

    • (post-multiplying by )