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Question

What is the shortcut to finding the determinant of a 5×5 matrix?


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Solution

The determinant is used in the square matrix and is a scalar value.

Laplace expansion is used to determine the determinant of a 5×5 matrix.

  • First, the cofactors of every number are found in that row and column, by applying the cofactor formula -1i+jAi,j, where i is the row number and jis the column number.
  • After that, the cofactor is multiplied by each number in that row or column.
  • Then the products are added up.

Assume a matrix A=200-3016461-200142003-240002

Select a row or column. Here take the second column and apply the formula.

6-12+220-30-2014203-24002

=620-30-2014203-24002

R4=R4×(R2+R3)

=620-30-2014203-20004

Select the fourth row, and apply the formula.

64-14+420-3-201203

=6420-3-201203

=2420-3-201203

R1=R1+R3

=24400-201203

Select the first row and apply the formula.

244(-1)1+10103

=2440103

=960103

Select the first row.

96-11+20

=96-10

=960

=0

So, the determinant is 0.


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