Find the value of `y` if `|[y,-1],[0,2]|=2|[1,-1],[0,2]|`

Find the values of x and y , if 2[(1, 3),( 0,x)]+[(y,0),( 1, 2)]=[(5, 6),( 1 ,8)] .

Find the values of x,y,a and b, if : [{:(,x-2,y),(,a//2,b+1):}]=[{:(,0,3),(,1,5):}]

Find the value of k if kx+ 3y - 1 = 0, 2x + y + 5 = 0 are conjugate lines with respect to the circle x^(2) + y^(2) - 2x - 4y - 4 =0 .

Find x and y, if 2[[1, 3],[ 0,x]]+[[y,0], [1, 2]]=[[5, 6],[ 1, 8]]

Find the value of the following: tan [1/2[sin^(-1) ((2x)/(1+x^2))+cos^(-1) ((1-y^2)/(1+y^2))]], |x| 0 and x y < 1 .

Find the value of K if the lines x+y-5=0 and 2x+ky-8=0 are conjugate with respect to the circle x^(2)+y^(2)-2x-2y-1=0

(i) Find the value of 'a' if the lines 3x-2y+8=0 , 2x+y+3=0 and ax+3y+11=0 are concurrent. (ii) If the lines y=m_(1)x+c_(1) , y=m_(2)x+c_(2) and y=m_(3)x+c_(3) meet at point then shown that : c_(1)(m_(2)-m_(3))+c_(2)(m_(3)-m_(1))+c_(3)(m_(1)-m_(2))=0

Find the values of x and y satisfying the equation: 2[[1,3],[0,x]]+[[y,0],[1,2]]=[[5,6],[1,8]]

Find X, if Y=[[3, 2],[ 1, 4]] and 2X+Y=[[1 ,0],[-3, 2]]

Find the value of a for which the lines 2x+y-1=0 , a x+3y-3=0 , 3x+2y-2=0 are concurrent.