

Prove or disprove the following. (a) R is a field. (b) There is
an additive identity for vectors in R^n. (If true, what is
it?)........
1. Prove or disprove the following. (a) R is a field (b) There is an it?) additive identity for vectors in R". (If true, what is (c) There is a is it? multiplicative identity for vectors in R". (If true, what (d) For , , (e) For a, bE R and E R", a(b) =...
3. Prove the following identity:
Xn
i=1
9
10i = 1 ?
1
10n :
1
3. Prove the following identity: n 1 9 10i = 1 - 10n' i=1
(2) Using the identity: n! k!(n - k)! for n > 2, prove that the following identity is even: 1 n
3. (a) Let z1,z2, z3 € C, prove the following identity: (21 - 22)(22 – 23)(23 – £1) = (22 - 23)+23(23 – £1)+23(21 - 22). (b) In AABC, P is a point on the plane II containing A, B and C. Prove that aPA +bPB2 +cPC2 > abc.
Prove Lagrange's identity, i.e. (a × b) . (c × d) = (a . c)(b . d)-(a . d)(b . c).
Prove the following vector identity using index notation A X (BXC) = (A.C)B - (A.B)C
Prove this identity
Linear Algebra (Introduction)
6. Prove the following identity
Prove by induction that for every positive integer n, the following identity holds: 1+3+5+...+(2n – 1) = np. Stated in words, this identity shows that the sum of the first n odd numbers is n’.
2. Prove the following identity. [5] sine+2sin? O cos? 0 + cose=1