Evaluate the determinants in Exercises and . . – . (i) –sin (ii) – – .
If A = , then show that | 2A | = | A | . If A = , then show that | A | = | A | . Evaluate the determinants (i) – – (ii) – – (iii) – – (iv) – – . If A = – – – , find | A | .
Find values of x , if (i) (ii) . If x = , then x is equal to (A) (B) ± (C) – (D) . Area of a Triangle In earlier classes, we have studied that the area of a triangle whose vertices are ( x , y ), ( x , y ) and ( x , y ), is given by the expression [ x ( y – y ) + x ( y – y ) + x ( y – y )]. Now this expression can be written in the form of a determinant as ∆ = ...
( ) Remarks (i) Since area is a positive quantity, we always take the absolute value of the determinant in ( ). (ii) If area is given, use both positive and negative values of the determinant for calculation. (iii) The area of the triangle formed by three collinear points is zero. Example Find the area of the triangle whose vertices are ( , ), (– , ) and ( , ).
Solution The area of triangle is given by ∆ = DETERMINANTS ( ) ( ) ( ) – – – – – – ( ) Example Find the equation of the line joining A( , ) and B ( , ) using determinants and find k if D( k, ) is a point such that area of triangle ABD is 3sq units. Solution Let