1 Determinants
Let and B = A2 . If (l – m)2 + (p – q)2 = 9, (m – n)2 + (q – r)2 = 16, (n – l)2 + (r – p)2 = 25, then the value of det. B equals.. 1) 100 2) 125 3) 144 4) 169
Solution
det. A is twice the area of the triangle with vertices (l , p), (m, q), (n, r) with sides 3, 4, 5.
D2 = s(s – a)(s – b)(s – c) D2 = 6(6 – 3)(6 – 4)(6 – 5) D2 = 36 =>D 6 Now det A =D 2 = 12 =>det. B = (det A)2 = 4D2 = 144
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