Please tell me how I can solve this assignment. It would better if I can learn step by step.

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. Determine whether the following subsets of 11' form a subspace or not: a} those vectors in FL'1 all of whose coordinates are between I] and 1; b) those vectors in IEL'I in which the rst coordinate equals the second. . Determine whether the following subsets of lit.15 form a subspace or not: a} those vectors in FL'3 in which the coordinates are increasing (from the top down), b) those vectors in lit'3 in which the sum of the upper three coordinates is the same as the sum of the lWEI' three. . [MT'12) Let's call a vector in R5 Fibonaccitype if all of its coordinates, starting form the third one, are sums of the previous two coordinates. (Eg. the vector {3,1,2,1,3}T is Fibonaccitype.) Do the Fibonaccitype vectors form. a subspace in R5? . [MT+'15) Let the set W consist of the vectors 2 E R5 for which it holds that the diEerence of an},r two coordinates of p is an integer. [E.g. the vector [3.,1.,4.,8.,.}T is like that.) Decide whether W forms a subspace in R5 or not. . [MT+'1fi) Do the vectors (r, le for which m2 = y\" holds form a subspace of R2? . [MT++'16} Do the vectors (r, y, of for which my 2 ye holds form. a subspace of R3? . [MT+'18) Let the set V consist of the vectors in R.\" for which it holds that the product of their four coordinates is greater than or equal to It]. Decide whether V forms a subspace in 11'1 or not. . [MT++'19) Let's call a vector y in R\" a pal-indrmne, if writing the coordinates of E in the reverse order we get y as well. [E.g. {5,1,2,1,5}T is a palindrome.) Show that the set of all the palindromes in R5 is a subspace of R5. . In R\" 1a a = [1,2,c,c}T, E = {c,1,2,c}T, a: = (as, 1,211\14. (MT+'17) Let u = (0, 0, 1, 2)", u = (0, 1, 2, 5)" and w = (1, 2, 4, 11)" be vectors in R4. Determine span z, v, w}, the subspace spanned by them. (That is, give a (system of) equation(s), satisfied by the vectors in span {u, v, w}.)17. (MT'19) Let u, u and w be the vectors in R' below. Determine all those elements of the generated subspace span {u, u, w} whose all the coordinates are equal. u = (1, 2, 0,0)7, v = (1, 0,3, 0), w = (1, 0, 0,4)?'