Let `A=[{:(x^(2),6,8),(3,y^(2),9),(4,5,z^(2)):}],B=[{:(2x,3,5),(2,2y,6),(1,4,2z-3):}]`. If trace A = trace B, then `x+y+z` is equal to ________

Let |{:(y^(5)z^(6)(z^(3)-y^(3)),,x^(4)z^(6)(x^(3)-z^(3)),,x^(4)y^(5)(y^(3)-x^(3))),(y^(2)z^(3)(y^(6)-z^(6)),,xz^(3)(z^(6)-x^(6)) ,,xy^(2)(x^(6)-y^(6))),(y^(2)^(3)(z^(3)-y^(3)),,xz^(3)(x^(3)-z^(3)),,xy^(2)(y^(3)-x^(3))):}| " and " Delta_(2)= |{:(x,,y^(2),,z^(3)),(x^(4),,y^(5) ,,z^(6)),(x^(7),,y^(8),,z^(9)):}| .Then Delta_(1)Delta_(2) is equal to

If 2x+3y=5, 2y+z=3, and x+5y+z=3 , then x =

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 A=[{:(9, 7, 3), (5, -1, 4), (6, 8, 2):}]" find "A^(-1) and hence solve the system of equations: 9x+7y+3z=6, 5x-y+4z=1, 6x+8y+2z=4 .

If X={1,2,3,4} , Y={2,3,5,7}, Z={3,6,8,9},W={2,4,8,10}, then

Find x ,\ y ,\ z ,\ t if 2[(x, z ),(y ,t)]+3[(1,-1),( 0, 2)]=3[(3, 5),( 4 ,6)] .

If A = [(5, -1, 4), (2, 3, 5), (5, -2, 6)] , find A^(-1) and use it to solve the following system of equation 5x - y + 4z = 5, 2x + 3y +5z = 2, 5x - 2y + 6z =-1

Comprehension 1 Let x ,\ y ,\ z in R^+&\ D=|xx^3x^4-1y y^3y^4-1z z^3z^4-1| If x!=y!=z\ &\ x ,\ y ,\ z are in A.P. and D=o,\ t h e n\ 2x^2z+x^2z^2 is equal to a. 1 b. 2 c. 3\ d. none of these

If x=2a^(2)+3b^(2)-5ab, y=b^(2)-3a^(2)+7ab and z=6a^(2)-b^(2)+ab , find: x+y-z