math 3

math 5

Explain why 4 | 0 but 0 + 4. Your response should make use of the definition of "divides". Keep in mind that "divides" means something different than "divided by".

Decide if the following are true or false: • true 5 = 2 (mod 3) • true 0 = 16 (mod 4) • false 9 = 10 (mod 3) • false -8 = 19 (mod 9).

Decide if each of the following are true or false: ⚫ false 4 | 13 ⚫ true -8 64 . ⚫ true 18 | 9 • ⚫ true 6 | 0 • • true 1 | −1

math  2

math 1

Q1/(a) Let f be a map from linear space X into linear space Y, show that whether each one of the statements trure or flase or not. 41) If A convex set of X then f(A) is a convex set of w 20 (2) If M is an affine subset of a space X and tEM then M-this an affine set Let R be a field of real numbers and X-M2(R) be a space of 2x2 matrices over R that whether there is a hyperspace of X or not. I love 00

21: A: Let f be a function from a normed space X in to a normed space Y. show that of continuous iff for any sequence (x,) in X convergent to xo then the sequence (f(x)) convergent to f(x) in Y. B: Let X be a vector space of dimention n isomorphic to a vector space Y. write with prove the dimension of Y. 32 22: A: Let X be a horned space of finite dimension .show that any two normone X are V equivalent. B: Let M2x3 be a vector space of 2×3. matrices on a field ? write wittraver convex set and hyperplane of M2x3 17 that