Linear Algebra Practice study problems forespecially problem #1True or False. (Need explanation on how to solve it). Thank you.

ID: Name: Discussion room: Midterm 2 practice No books. notes, or other aids are allowed. Show all your work for full credit. 1. (30 points) This part consists of 15 true-false questions. In each case answer true if the state- ment is always true and false otherwise. You do not need to provide any explanation. (a). The vectors 1'1,\"- ,1!" span 1R4, then n 2 4. (b). The vectors 121, - - - ,1)" is a basis of Rm, then 11 must equal to m. (c). If A is an n x m matrix and Rank(A) = m, then dimNul(A) = 0. (d). If A is an n, X 77, matrix, then A is invertible if and only if A is onetoone. (e). If A is an n x m matrix, then AT 7E A. (L (f). Let T : R2 > R be a linear transformation with T('1) = T('2) = 1, then T( [b )=a+h (g). Let T : R4 > R4 be a linear transformation, then T is not onetoone. (h). Let T : R" > Rm be a linear transformation, then T is one-toone if and only if Rank(A) = m where A is the standard matrix of T. (i). If A is an n x 71. matrix, then A is invertible if and only if Rank(A) = n. (.l)- { [] , [] . [(1)] } is a basis for R2. 2. (10 points) Let T : R2 > R3 be a linear transformation, moreover was ma Find the standard matirx of T. OOH OIlO Math 3A Midterm 1