| x a x + Prove, except using and distributing the determinant property: by + b [= 0 z cztc

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

By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],[b,c,0]|=0

If (x, y), (a, 0), (0, b) are collinear, then using determinants prove that x/a + y/b = 1 .

15.Using properties of determinants,prove the following b+c+aa+b

By using properties of determinant prove that |(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0

If (x,y),(a,0),(0,b) are collinear,then using determinants prove that (x)/(a)+(y)/(b)=1

If a+b+c ne 0 and |{:(a,b,c),(b,c,a),(c,a,b):}|=0 , then using properties of determinant, prove that a=b=c

IF a+b+c ne 0 and {:|(a,b,c),(b,c,a),(c,a,b)| =0, then using properties of determinants, prove that a=b=c

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: |0a-b-a0-c b c0|=0