Use the Cofactor Expansion Theorem to evaluate the given det

Use the Cofactor Expansion Theorem to evaluate the given determinant along row 1. |1 -2 1 3|

Solution

Along Row 1 = M11 (element obtained by deleting the first row and first column), which is 3

M11 = 3

Similarly M12 = 1

Determinant of 2X2 matrix = aij*Mij (if i+j is even), else -aij * Mij(if(i+j) is odd)

=> 1 * 3 -(-2) * 1

=>3 + 2

=> 5

Hence the determinant of the matrix is equal to 5