(iii) सारणिक का बिना विस्तार किये हुए सिद्ध करें कि `|{:(a,b,c),(x,y,z),(p,q,r):}|= |{:(y,b,q),(x,a,p),(z,c,r):}|=|{:(x,y,z),(p,q,r),(a,b,c):}|`

Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, a, p), (z, c, r):}|

If A = |(a,b,c),(x,y,z),(p,q,r)| and B = |(q,-b,y),(-p,a,-x),(r,-c,z)| , then

Without expanding, prove that : |{:(1+b,b+c,c+a),(p+q,q+r,r+p),(x+y,y+z,z+x),(x+y,y+z,z+x):}|=2|{:(a,b,c),(p,q,r),(x,y,z):}|

If Delta=|(a,p,x),(b,q,y),(c,r,z)|=16 then Delta_(1)=|(p+x,a+x,a+p),(q+y,b+y,b+q),(r+z,c+z,c+r)|=32

Let X = {a,b,c,p,q,r,x,y,z}, A= {b,q,y}, B={a,p,r,x,y} then (A nn B)'

Without expansion, prove the following: |(a+b, b+c, c+a),(p+q, q+r, r+ p),(x+y, y+z, z+x)|=2|(a,b,c),(p,q,r),(x,y,z)|

Consider the following relations from A to B where A={u, v, w, x, y, z} and B={p, q, r, s}. 1. {(u,p),(v,p),(w,p),(x,q),(y,q),(z,q)} 2. {(u,p),(v,q),(w,r),(z,s)} 3. {(u,s),(v,r),(w,q),(u,p),(v,p),(z,q)} 4. {(u,q),(v,p),(w,s),(x,r),(y,q),(z,s)} Which of the above relations are not functions ?

Use the properties of determinant and without expanding prove that |{:(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):}| .