6 image of x under 4. Problem 2: With the transformation T(x)- AX, and the vector b T, find if it exists. (13 points...
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
Question 1: T defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. 0 -2 -1 A = -2 6 b 7 3 -2 -5 -3 1 1
If T is defined by T(x) = Ax, find a vector x whose image under T is b and determine whether x is unique.Find a single vector x whose image under T is b
13. A linear transformation T takes Nº into f". T[ +y - y 2.1 + 3y y (a) Is T one to one? Justify your answer. If not, then give two vectors with the same image. (b) Is T onto? Justify your answer. If not then give a vector in R? that is not an image.
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.
12 For problems 6 through 10, let A= 0 4 and let T be the linear transformation 3 1 defined by X → Ax. 6. 7. 8. 9. 10. What is the domain of T? Justify your answer. What is the codomain of T? Justify your answer. Describe the range of T. Is T one-to-one? Justify your answer. Is T onto? Justify your answer.
(d) (4 points) Let T : R² + Rº be the transformation that rotates any vector 90 degrees counterclockwise. Let A be the standard matrix for T. Is A diagonalizable over R? What about over C? (e) (3 points) Let T : R4 → R4 be given by T(x) = Ax, A = 3 -1 7 12 0 0 0 4 0 0 5 4 0 4 2 1 Is E Im(T)? 3 (f) (9 points) Let U be a...
Find all x in R that are mapped into the zero vector by the transformation x Ax for the given matrix A. 111 13 A 0 1-4 4 4 -16 28-36 Select the correct choice below and fill in the answer box(es) to complete your choice. O A. There is only one vector, which is x- + X 3
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 is a linear transformation that maps vectors x in 975 into vectors Let A= 0 -2 1 b in R2 Consider the set of all possible vectors b-Ax, where x is of unit length. What is the longest vector b in this set, and what unit length vector x is used to obtain it? You can use Matlab to save time with the computations, but please justify your answer. , A is a linear transformation that maps vectors...