3 x 3 Determinants A Short Cut Method By Dr. Julia Arnold There are short cut methods of finding the determinant for the 2x2 matrix and the 3x3 matrix. All square matrices of size 4 and above must use the Cofactor and Minors method of finding the determinant. Dr. Burger, in his notes, has shown you the Cofactor method for the 3x3 determinant and at the beginning of the notes he shows the short cut method which may appear confusing. I would like to show you an easier version of the short cut method for finding determinants for a 3x3 matrix. We will use the same example that is in the notes: Example 2 3 1 1 1 1 0 4 2 From the notes we already know the answer is -14 Here is the easy way to arrive at that answer: Step 1: Copy column 1 and 2 next to the matrix. 2 3 1 1 1 1 02 4 3 2 1 1 1 1 Step 2: Beginning with 2, multiply the numbers on the diagonal (3 numbers only). 2 3 1 1 1 1 02 4 3 2 1 1 To that add the product of the 3 numbers on the next diagonal. 1 1 2 ( 1 )2 1 ( 4 )( 1 ) 0 (3 )( 1 ) 4 4 0 0 And again, the product of the 3 numbers on the last diagonal. Now beginning with the 1 in the upper right hand corner, we are going to come back, multiplying the numbers on the diagonals. We will also sum these and then subtract the answer from the sum above. 2 3 1 1 1 1 02 4 3 2 1 1 1 1 (3 )( 2 ) 2 ( 4 )( 1 ) 0 ( 1 )( 1 ) 6 8 0 14 1 Now subtract: 0 - 14 = - 14

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# 3 x 3 Determinants A Short Cut Method