8 x+y + 2z =4 x+2y + z =1 x+y+z = 2

2x + 3y + z = 11, x + 2y + z = 8, x-y + z = 2

Find the angle between the planes : (i) 3 x - 6y - 2z = 7 " " 2x + y - 2z = 5 (ii) 4 x + 8y + z = 8 " " and y + z = 4 (iii) 2 x - y + z =6 " " and x + y + 2z = 7 .

Prove that Det [[x + y + 2z, x, y], [z, y + z + 2x, y], [z, x, z + x + 2y]] = 2 (x + y + z) ^ 3

Using matrices, solve the following system of equations for x,y and z. 3x-2y+3z=8 , 2x+y-z=1 , 4x-3y+2z=4

If sin ^ (- 1) x + sin ^ (- 1) y + sin ^ (- 1) z = pi show that, x ^ (4) + y ^ (4) + z ^ (4) + 4x ^ ( 2) y ^ (2) z ^ (2) = 2 (x ^ (2) y ^ (2) + y ^ (2) z ^ (2) + z ^ (2) x ^ (2))

If sin ^ (- 1) x + sin ^ (- 1) y + sin ^ (- 1) z = pi, show that x ^ (4) + y ^ (4) + z ^ (4) + 4x ^ ( 2) y ^ (2) z ^ (2) = 2 (x ^ (2) y ^ (2) + y ^ (2) z ^ (2) + z ^ (2) x ^ (2))

3x+4y+7z=4, 2x+y+ 3z= 3, x + 2y +3z =8.

2x+8y+5z=5 x+y+z=-2 x+2y-z=2

If z = sec ^ (- 1) ((x ^ (4) + y ^ (4) -8x ^ (2) y ^ (2)) / (x ^ (2) + y ^ (2))) then x (from z) / (from x) + y (from z) / (from y) =