Evaluate the determinant using the row or column that minimi

Evaluate the determinant using the row or column that minimizes the amount of computation.

Evaluate the determinant using the row or column that minimizes the amount of computation.

Solution

Here the determinant using column 3 minimizes the comptuation required to find the det value since it contains two zeroes out of three column values.

Hence determinant of Matrix given =

0 * det [ 2 5 ; 3 4] - (-2) * det [1 3 ; 3 4] + 0 * det [1 3 ; 2 5] = 2 * det [1 3 ; 3 4]

= 2 *( 1 * 4 - 3* 3) = 2 * ( 4-9) = 2* (-5) = -10.

Hence the answer is -10.

Here I used the denotion [ a b; c d] to denote a matrix 2 * 2 matrx with a , b as the values in the first row and c , d as the values in the second row. The \";\" (Semicolon) seperates rows from each other.