Exercise 2. True or False (give a counterexample when False) a. The vectors b that are not in column space C(A) form a subspace. b. If C(A) contains only the zero vector, then A is the zero matrix. c. The column space of 2A equals the column space of A. d. If A is a square matrix, the column space of A – I equals the column space of A.
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- The vector x ∈ R N has L different entries. For example, L = 4 for x = [3,4,4,5,3,1,5,3]T . One can express x as x = S u, where u ∈ R L satisfies (u)i < (u)j if i < j and S is a matrix that contains only zeros and ones. Write the function repeated_entries, which takes x as input and returns S and u.Implement the following function, without using any data structure. /* Given two vectors of chars, check if the two vectors are permutations of each other, i.e., they contains same values, in same or different order.e.g., V1=[‘a’,’b’,’a’] and V2=[‘b’,’a’,’a’] stores same multi-set of data points: i.e., both contains two ‘a’, and one ‘b’. e.g., V3=[‘a’,’c’,’t’,’a’] and V4=[‘a’,’c’,’t’] are not same multi-set. V3 contains two ‘a’s, while V4 has only one ‘a’. Note: when considering multiset, the number of occurrences matters. @param list1, list2: two vectors of chars @pre: list1, list2 have been initialized @post: return true if list1 and list2 stores same values (in same or different order); return false, if not. */ bool SameMultiSet (vector<char> list1, vector<char> list2)What to input here to run properly? % Encode the Matrix A and the column vector b. A= b= % Solve for Determinant of A. Set as dA. dA = % Find the Inverse of A. set as iA. iA = % Form the Reduced Row Echelon of A. Set as rA. rA= %Find the number of rows and number of columns of Ab. set as rowA and colA. % Find the sum of the columns of A. Set as SumA. %In each of the columns of A, find the highest values and its indices.Set as highA and locA. %Augment A with b; Set as Ab. % Find b\A. Set as Root1. %Form the Reduced Row Echelon Form of Ab. Set as refAb. %Extract the last column of refAb.Set as Root2. %Create a matrix A whose elements are the same as matrix A, but the first column is the column vector b. Set as Ax. %Create a matrix A whose elements are the same as matrix A, but the second column is the column vector b. Set as Ay. %Create a matrix A whose elements are the same as matrix A, but the third column is the column vector b. Set as Az. %Create…
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