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MATHEMATICS

JAMB 2011 - Question 25

Mathematics 2011 JAMB Past Questions - Question 25: Evaluate |4 2 -1| 2 3 -1 -1 1 3

Evaluate |4 2 -1| 2 3 -1 -1 1 3

A: 25

B: 45

C: 15

D: 55

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Correct Answer

Explanation

4<(3x3) - ( - 1x1)> - 2 <2x3) - (-1x-10)> -1 <(2x1)-(1x3)>= 4<9+ 1> -2 <6-1> - 1 <2+3>= 4 (10) -2 (5) -1 (5)= 40 - 10 -5= 25To evaluate the determinant of the given matrix:|4 2 -1||2 3 -1||-1 1 3|We can use the formula for a 3x3 determinant:|a b c||d e f||g h i| = a(ei - fh) - b(di - fg) + c(dh - eg)Substituting the values from the given matrix:|4 2 -1||2 3 -1||-1 1 3| = 4(3 * 3 - (-1) * 1) - 2(2 * 3 - (-1) * 1) + (-1)(2 * 1 - 3 * (-1))Simplifying the expression:= 4(9 + 1) - 2(6 + 1) + (-1)(2 + 3)= 4(10) - 2(7) - 1(5)= 40 - 14 - 5= 21Therefore, the determinant of the given matrix is 21.