The determinant `|x p+y x y y p+z y z0x p+y y p+z|=0` if `x ,y ,z`

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonzero real number, is equal to a. x y z b. 2x y z c. 3x y z d. 4x y z

The repeated factor of the determinant |(y +z,x,y),(z +x,z,x),(x +y,y,z)| , is

By using properties of determinants. Show that: |[x,x^2,y z],[ y, y^2,z x],[ z, z^2,x y]|=(x-y)(y-z)(z-x)(x y+y z+z x)

Prove that sin (x + y ) sin (x -y) + sin ( y+ z) sin (y - z) + sin (z+x) sin (z-x) = 0.

Using properties of determinants, prove that |(a+x, y, z),(x, a+y, z),(x, y,a+z)|=a^2(a+x+y+z)

For every point P(x ,\ y ,\ z) on the xy-plane, a. x=0 b. y=0 c. z=0 d. x=y=z=0

For every point P(x ,\ y ,\ z) on the xy-plane, a. x=0 b. y=0 c. z=0 d. x=y=z=0

If x,y, z are in A.P., then the values of the determinant |(a +2,a +3,a + 2y),(a + 3,a +4,a + 2y),(a +4,a +5,a + 2z)| , is