" 1.Without expanding the determinant,prove that "|[x,a,x+a],[y,b,y+b],[z,c,z+c]|=0

Without expanding the determinant prove the following. |[x,a,x+a],[y,b,y+b],[z,c,z+c]|=0

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

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

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

Without expanding the determinant , prove that |{:(ax,by,cz),(x^2,y^2,z^2),(1,1,1):}|=|{:(a,b,c),(x,y,z),(yz,zx,xy):}|

Using the property of determinants and without expanding in questions 1 to 7 prove that , |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0

Using the property of determinants and without expanding in questions 1 to 7 prove that , |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0

Without expanding the determinant prove the following. |[b+c,q+r,y+z],[c+a,r+p,z+x],[a+b,p+q,x+y]|=2|[a,p,x],[b,q,y],[c,r,z]|

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

Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=0 .