Answer :
The determinant of the given matrix { [1 4 3], [3 5 1], [4 1 5]} is -71. Thus, the correct answer is (d) -71.
To compute the determinant of the matrix using cofactor expansion, we can expand along the first row:
det = 1( det ([5 1][1 5]) - 4 ( det([3 1][4 5]) ) + 3 ( det([3 5][4 1]) )
det = 1(( 5*5 - 1*1 ) - 4*( 3* 5 - 1*4 ) + 3*( 3*1 - 5*4 ))
det = 1( 25 - 1 - 4 ( 15 - 4 ) + 3 ( 3 - 20 ))
det = 1( 25 - 1 - 4 ( 11 ) + 3 (-17) )
det = 1( 25 - 1 - 44 - 51 )
det = 1( -71 )
Therefore, the determinant of the given matrix is -71.
So, the correct answer is (d) -71.
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