(1 point) If T:R → R is a linear transformation such that 13 , T||0||= 01)...
(1 point) If T:R? → R is a linear transformation such that -0-0-0-0-0-0) then
11.) Let T:R" - R"be a linear transformation. Prove T is onto if and only if T is one-to-one. 12.) Let T:R" - R" and S:R" - R" be linear transformations such that TSX=X for all x ER". Find an example such that ST(x))+x for some xER". - .-.n that tidul,
1. (a) Let T:R' R'be defined by T(x) = 5 -2. Is T a linear transformation? If so, prove that it is. If not, explain why not. (b) More generally than part (a), suppose that T:R → R is defined by T(x) = ax +b, where a and b are constants. What must be true about a and b in order for T to be a linear transformation? Explain your answer.
Let A= and 6 = Define the linear transformation T:R? +R by T'(X) = Ai. Find a vector # whose image under T' is 6. Is the vector i unique choose choose unique Submit answer not unique
A Linear transformation T:R^5→R^4 is given as How do I find the standard matrix of T, the zero space and column-space of T? How do I find the rank and the dimension of the zero-space of T? C1 x2 1 as C2 + 4- x5 C4 C5
T:R R2 is a linear transformation with T(1,0, 2) = (2, 1) and T(0,1,-1) = (-5,2). It follows that T(2, -3,7) is equal to Select one: 0 a. (-11, -8) O b. (2, 3) c (19, -1) d. not enough information is given to determine the answer e(-3,3)
1. Is T a linear transformation? Justify completely a. T:R → RP defined by T(1, y, z) = (y, 1-22, y) b. T:R + P, defined by T(a,b,c) = (a - cr? - bx +1
true or false The linear transformation T:R? R? defined by T'(x,y) = (x + y,X-V) is invertible.
13. (Linear Algebra Review) Recall that a function T:R" + R" is one-to-one if for each b ER", there is at most one x ER" such that T(x) = b. Let T be a linear transformation given by a matrix A. If T is one-to-one, then what can be said about the columns of A? What can be said about the determinant of A?
(1 point) Find the matrix M of the linear transformation T:R? → Rgiven by - 1-5xı +(-8)x2] 2x1 - x2] M =