[" (6) show thal "," a "," b "," C "],[,," a "+2x," b+2y "," c "+2z,=0]

|{:(" "a," "b," "c),(" "a+2x," "b+2y," "c+2z),(" "x," "y," "z):}|

prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

By using properties of determinants , show that : (i) {:|( a-b-c, 2a, 2a),( 2b, b-c-a, 2b ) , ( 2c,2c, c-a-b) |:} = ( a+b+c)^(3) (ii) {:|( x+y+2z, x,y ),( z, y+z+2x, y ),( z,x,z+x+2y )|:} =2( x+y+z)^(3)

Show that |a b c a+2x b+2y c+2z x y z|=0

Show that |a b c a+2x b+2y c+2z x y z|=0

Prove that |[a x-b y-c z, a y+b x, c x+a z], [a y+b x, b y-c z-a x, b z+c y],[c x+a z, b z+c y, c z-a x-b y]|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

Prove that |[a x-b y-c z, a y+b x, c x+a z], [a y+b x, b y-c z-a x, b z+c y],[c x+a z, b z+c y, c z-a x-b y]|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

Without expanding , show that |(a,b,c),(a+2x,b+2y,c+2z),(x,y,z)|= 0 .

Show that abs((a,b,c),(a+2x,b+2y,c+2z),(x,y,z)) =0

Show that |{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0