T:R R2 is a linear transformation with T(1,0, 2) = (2, 1) and T(0,1,-1) = (-5,2)....
T:R3 → 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. (7,1) O O b. not enough information is given to determine the answer C. (-11, –8) O d. (2, -3) o e. (19,-4)
4. T: R2 + R2 is a function such that T(1,1)= (1,0) and T(1, -1) = (0,1). (a) (3 marks) If T is a linear transformation, calculate T(3,1). (b) (2 marks) If T(2,0) = (2, 2), prove that T is not a linear transformation.
Let T: P2 --> R2 be the linear transformation such that T(x+1)=(1,1), T(x2)=(1,0) and T(x-1)=(0, 1). Find T(2+x+x2).
(1 point) If T:R → R is a linear transformation such that 13 , T||0||= 01) [ 1] T||1||= -1, Uo4 -4 i 2 1 T||0||= (11) then T|| -2
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. 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
caution!! please ignore this question. it is uploaded accidentally. thanks Let ē- (1,0), 2, - (0,1), 1 = (-5, -7) and 2: - (-4,6). Let T:R? Rº be a linear transformation that sends ēj to 2, and ēs to 23. If T maps (2, 3) to the vectory, then (Enter your answer as an ordered pair, such as (1.2), including the parentheses.)
Is the transformation, T, given below a Linear Transformation where T: R2 -> R2 [:] - [+*] (y + 1)2 1 x - 1 1
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square and let RCR be the parallelogram with vertices (0,0), (2, 2), (3,-1), (5,1). a. Find a linear transformation T:R2 + R2 such that T(S) = R and T(1,0) = (2, 2). What is T(0, 1)? T(0,1): 2= y= b. Use the change of variables theorem to fill in the appropriate information: 1(4,)dA= S. ° Sºf(T(u, v)|Jac(T)| dudv JA JO A= c. If f(x, y)...
DETAILS LARLINALG8 6.R.013. Determine whether the function is a linear transformation. T: R2 – R2, T(x, y) = (x + h. y + k), h + 0 or k + 0 (translation in R2) linear transformation not a linear transformation If it is, find its standard matrix A. (If an answer does not exist, enter DNE in any cell of the matrix.) 11