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Let A= and 6 = Define the linear transformation T:R? +R by T'(X) = Ai. Find...
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
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 point) Let 1-11 ſi -1 31 A = 0 1 -1 and b=1-2 L-1 -2 0 [7] Define the linear transformation T:R* R* by T(T) = A. Find a vector a whose image under T is b. Is the vector i unique? choose choose unique Note: In order to get cred not unique all answers must be correct
(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
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 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
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
true or false The linear transformation T:R? R? defined by T'(x,y) = (x + y,X-V) is invertible.
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
:| Let T : P → R , such that T (ao +ax+a2x2 +a3r)-4 +ai +a, +a3 . a) Prove that T is a linear transformation b) Find the rank and nullity of T. c) Find a basis for the kernel of T. :| Let T : P → R , such that T (ao +ax+a2x2 +a3r)-4 +ai +a, +a3 . a) Prove that T is a linear transformation b) Find the rank and nullity of T. c) Find a...