Please show me step by step thanks a Prove that if C1 C2 c1

Please show me step by step... thanks

(a) Prove that if (C1 + C2, c1 - e2) = 0, then c1 = = 0. (proving this requires p > 2). 5. Let p > 2 be an odd prime number. Work over F = Z/(pZ). Let C1 be a linear code with parameters [n, k1, d1] and C2 a linear code with parameters [n, k2, d2]. Assume d1 = > d2. Let {b1... Bk1} be a basis for C1 and {e1 ... ,ek2} a basis for C2. Let C1 oC2 be the code consisting of words (c1 + c2,c1 - c2) where c1 belongs to C1 and c2 belongs to C2. You may assume without proof that this code is linear

Solution

(c1+c2, c1-c2)=0

implies that c1+c2=0 and c1-c2=0

solving this equations we get c1=0 and c2=0