Previous Problem Problem List Next Problem (1 point) Let 07 A = -5 6 6 and b -3 3 -2 L 9 -437 96 R4 by T) = AE. Find a vector ã whose image under T is . Define the linear transformation T: R3 Is the vector i unique? choose Note: In order to get credit for this problem all answers must be correct
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
(1 point) Let [ 4 51 [ 51 A = -1 -2 and b = 1 : 1-3 -3] 1-6] Define the linear transformation T : R2 → R3 by T(x) = Añ. Find a vector à whose image under T is b. Is the vector x unique? choose
(1 point) Let 6 -5 5 16 47 5 4 6 A= and b= 3 3 11 -4 -3 -8 116 40 Define the transformation T:R? R4 by T(2) = Ax. Find a vector x whose image under T is b. = Is the vector x unique? unique
Define the linear transformation T:?3??4 by T(x )=Ax . Find a vector x whose image under T is b (1 pt) Let 4 5 2 -2 5 -3 2 and b-10 -7 2 1 -4 Define the linear transformation T : R3 ? R4 by T(x-Ax Find a vector x whose image under T is b. x= Is the vectorx unique? choose
Let L in R 3 be the line through the origin spanned by the vector v = 1 1 3 . Find the linear equations that define L, i.e., find a system of linear equations whose solutions are the points in L. (7) Give an example of a linear transformation from T : R 2 → R 3 with the following two properties: (a) T is not one-to-one, and (b) range(T) = ...
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.
[1 41 and we [-121 (1 point) Let A= 3 12 Find k so that there exists a vector x whose image under the linear transformation T(x) = Axis w. Note: The image is what comes out of the transformation. k= Find k so that w is a solution of the equation Ax = 0
(1 point) Let 5 -15 50 A=1-1 2 4 | and b=I-12 4 16 」 A linear transformation T : R2 → R3 is defined by T x) = Ax. Find an x in R2 whose image under T is b. X2
4 1 0 -3 1 If T is defined by Tix)= Ax, find a vector x whose image under Tis b, and determine whether x is unique. Let A and Find a single vector x whose image under Tis b.