Show without expanding at any stage that: `det [ [a,b,c],[a+2x,b+2y,c+2z],[x,y,z]] =0 `

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

Show without expanding at any stage that: [x,a,x+a],[y,b,y+b],[z,c,z+c]|=0

Show without expanding at stage that : det[[1,ca,b(c+a)1,ab,c(a+b)]]=0

Show without expanding at any stage that: [x+y,y+z,z+x],[z,x,y],[1,1,1]|=0

Without expanding at any stage, find the value of : |{:(,a,b,c),(,a+2x, b+2y, c+2z),(,x,y,z):}|

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

Without expanding , 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

Using the property of determinants and without expanding prove the following |{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0

Using the property of determinants and without expanding, prove that: |[x, a ,x+a],[ y, b, y+b],[ z, c, z+c]|=0