Steel vas of die vole gender matriksoperatore op Rn met n Gr

Steel vas of die vole gender matriksoperatore op R^n (met n Greaterthanorequalto 2) even-tot-even is./Determine whether the following matrix operators on R^n (with n Greaterthanorequalto 2) are one-to-one. T(x_1,x_2,...,x) = (0,x_1,x_2,...,x_n 0 T(x_1,x_2, ,X_n) = (x_n,X_n_1, . . . ,X_2,X_1) T(X_1,X_2, . . . ,X_n) = (X_2,X_3,. . . ,X_n,X_1) T(x_1,x_2, . . . ,X_n) = (X_1 + X_2,X_2 + X_3, . . . ,X_n_1 + X_n, + X_1)

Solution

(a) This Matrix operator is not one to one because, we are getting more than n outcomes for n inputs.

(b) This Matrix operator is definitely one to one because we are getting n outcomes for n inputs.

(c) This Matrix operator is as well one to one because we are getting n outcomes for n inputs.

(d) This Matrix operator is also one to one because we are getting n outcomes for n inputs. Note that (x1+x2) is one outcome.

(e) This Matrix operator is as well one to one because we have n number of outcomes for n inputs.

Therefore, except for (a), all other Matrix Opeartors are one to one.