Let D = diag `[d_1,d_2,d_3]` where none of `d_1,d_2,d_3` is 0. prove that: `D^-1=diag [d_1^-1,d_2^-1,d_3^-1]`.

If A = diag (d_1,d_2,d_3,….d_n) then det A is equal to

If P = [(d_(1),0,0),(0, d_(2),0),(0,0,d_(3))] then Adjoint (P) is equal to

Find the 3rd term of A.P if a=1 , d=2

If A = diag [1,-2,3] B = diag [3,4,-6] and C = diag [0,1,2], find A - 2 B + 3C

If y =(ax +b)/( cx + d) , then prove that 2y_1y_3=3(y_2)^2

Show that the plane ax+by+cz+d=0 divides the line joining (x_1, y_1, z_1) and (x_2, y_2, z_2) in the ratio of (-(ax_1+ay_1+cz_1+d)/(ax_2+by_2+cz_2+d))

Let A = {1, 2, 3}, then the number of equivalence relations containing (1,2) is (a) 1 (b) 2 (c) 3 (d) 4 .

Let a_1x+b_1y+c_1z+d_1=0 and a_2x+b_2y+c_2z+d_2=0 be two planes, where d_1, d_2gt0 . Then, origin lies in acute angle, If a_1a_2+b_1b_2+c_1c_2lt0 and origin lies in obtuse angle if a_1a_2+b_1b_2+c_1c_2gt0 . Further point (x_1, y_1, z_1) and origin both lie either in acute angle or in obtuse angle. If ( a_1x_1+b_1y_1+c_1z_1+d_1)(a_2x_1+b_2y_1+c_2z_1+d_2)gt0 . one of (x_1, y_1, z_1) and origin in lie in acute and the other in obtuse angle,If ( a_1x_1+b_1y_1+c_1z_1+d_1)(a_2x_1+b_2y_1+c_2z_1+d_2)lt0 Q. Given that planes 2x+3y-4z+7=0 and x-2y+3z-5=0 . If a point P(1, -2, 3), then a. O and P both lie in acute angle between the planes b.O and P both lies in obtuse angle c.O lies in acute angle, P lies in obtuse angle d. O lies in obtuse angle, P lies in acute angle

Statement 1: Distance of point D( 1,0,-1) from the plane of points A( 1,-2,0) , B ( 3, 1,2) and C( -1,1,-1) is 8/sqrt229 Statement 2: volume of tetrahedron formed by the points A,B, C and D is sqrt229/ 2

Two different non-parallel lines cut the circle |z| = r at points a, b, c and d , respectively. Prove that these lines meet at the point z given by (a^-1+b^-1-c^-1-d^-1)/(a^-1b^-1-c^-1d^-1)