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 by:

What is the minor? of an element in a 3x3 matrix?

• For any?element?in a 3x3 matrix, the?minor?is the determinant of the 2x2 matrix created by crossing out the row and column containing that?element
• For the matrix
  • The?minor?of the?element?a?would be found by:
    • crossing out the first row and first column
    • finding the determinant of the remaining 2x2 matrix
  • The?minor?of the?element?f?would be found by:
    • crossing out the second row and third column
    • finding the determinant of the remaining 2x2 matrix

How do I find the determinant of a 3x3 matrix?

• Finding the determinant of a 3x3 matrix is best explained using an example
• STEP 1
  Select?any row?or?column?in the matrix
  • e.g.? Selecting Row 2 of
• STEP 2
  Use the?matrix of signs ?to find the row or column that corresponds to the row or column selected in Step 1
  • e.g. ?Row 2 was selected so “-? +? -“ will be needed
• STEP 3
  Multiply?each?element?in the selected row or column by its?minor?and use the corresponding signs form the matrix of signs to determine whether to?add or subtract?each product
  • e.g.
• STEP 4
  Evaluate the?minors?and calculate the?determinant
  • e.g.
  • Check the answer using a calculator with a matrix feature

What are the properties of determinants of matrices?

• 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)
  • 
  • 

• If ?then?A?is singular
• If ?then?A?is non-singular