1) Give one example of a non-zero matrix A with at least 15 rational entries where the number of rows is larger than the number of columns and its row reduced echelon form. You must use your CSU ID digits or double digits to create matrix entries (use the order they appear in the CSU IDs list above). Write A and gref(A) in the space below. #USE: 2791805 AND SHOW WORK** a) The matrix A represents a transformation, rewrite the transformation indicating Domain and Codomain, that is, T: Ban to Bom (specify the values for n and m) T(X1, X2, X1, Xa, ......)=(21 1 X +312 X2+213 X3+..., azi Xi+azz X2 ,-..). Feel free to use x, y, ... instead of X1, X2, ...b) Are the columns of A independent? (Yes/No). If the answer is No, write a non-trivial linear combination of all columns that results in the zero vector. If the answer is Yes, what can you say about the solution of any linear combination of the columns of A that results in the zero vector? c) Give a basis for the Range of the transformation, that is the col(A) space. Do not forget to use set notation. What vectors in the column space look like? (That is, write all of them as a single vector using as many arbitrary constants as needed) d) Give an example of a vector in the col(A). What was your choice for the arbitrary constants? e) Give an example of a vector not in the col(A) (if there is one) or briefly justify why such vector can't be found.f) Use the representation in (c) to show that col(A) is indeed a vector space. Just show closure under addition, closure under multiplication and argue the reason that the zero vector in in col(A). Use other pages as needed. g) What vectors in the kem(T), that is, null(A) look like? Write a basis for the null space of A, if it exist. if Use the representation in (j) to show that null(A) is indeed a vector space. Just show the closure and zero vector properties. Attach other pages as needed. 2) Give one example of a non-zero square matrix C with at least 9 rational entries and its row reduced echelon form. Write a transformation associated to the matrix C and calculate both the kernel and the range of the transformation and state their dimensions. Attach pages as needed