If `[[1,3],[2,-1]][[x],[y]]=[[4],[1]]` then x and y is

Determine the product [[-4, 4, 4], [-7, 1, 3],[5, -3, -1]][[1, -1, 1],[1, -2, -2],[2, 1, 3]] and use it to solve the system of equations x – y + z = 4, x – 2y – 2z = 9, 2x + y + 3z = 1

If [(1,3,3),(1,4,4),(1,3,4)][(x),(y),(z)]=[(1),(2),(-3)], then the values of x, y and z respectively are

If |[ x y 1 1 ]|=2 and |[ x 3 y 2 ]|=1 then

If 2x-1/(3x)=y then 9x^2+1/(4x^2) in terms of y is

If the co-ordinates of the vertices of an equilateral triangle with sides of length a are (x_1,y_1), (x_2, y_2), (x_3, y_3), then |[x_1,y_1,1],[x_2,y_2,1],[x_3,y_3,1]|=(3a^4)/4

If the circle x^2 + y^2 = a^2 intersects the hyperbola xy=c^2 in four points P(x_1, y_1), Q(x_2, y_2), R(x_3, y_3), S(x_4, y_4) , then : (A) x_1 + x_2 + x_3 + x_4 = 0 (B) y_1 + y_2 + y_3 + y_4 = 0 (C) x_1 x_2 x_3 x_4= c^4 (D) y_1 y_2 y_3 y_4 = c^4

A triangle has vertices A_(i) (x_(i),y_(i)) for i= 1,2,3,. If the orthocenter of triangle is (0,0) then prove that |{:(x_(2)-x_(3),,y_(2)-y_(3),,y_(1)(y_(2)-y_(3))+x_(1)(x_(2)-x_(3))),(x_(3)-x_(1) ,,y_(3)-y_(1),,y_(2)(y_(3)-y_(1))+x_(2)(x_(3)-x_(1))),( x_(1)-x_(2),,y_(1)-y_(2),,y_(3)(y_(1)-y_(2))+x_(3)(x_(1)-x_(2))):}|=0

If x=2,y=1 then x^(4)+2x^(3)y-2xy^(3)-y^(4) is equal to

STATEMENT-1: If three points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are collinear, then |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=0 STATEMENT-2: If |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=0 then the points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) will be collinear. STATEMENT-3: If lines a_(1)x+b_(1)y+c_(1)=0,a_(2)=0and a_(3)x+b_(3)y+c_(3)=0 are concurrent then |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=0

If (x_(1)-x_(2))^(2)+(y_(1)-y_(2))^(2)=144,(x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=25 and (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=169, then the value of det[[x_(1),y_(1),1x_(2),y_(2),1x_(3),y_(3),1]]^(2) is 30(b)30^(2)(c)60(d)60^(2)