Given real numbers a and b, find a linear transformation T:R^3→R^3 such that the range of T is the plane z=ax+by.
Given real numbers a and b, find a linear transformation T:R^3→R^3 such that the range of...
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
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
(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
Consider the matrix transformation T:R → R given by T(x,y,z) = (x+ay, x+(a+1)y, x+ay+z) where a = 13. First use inverse of transformation to find T-(2,1,2). if T-(2,1,2)=(b,c,d) then b+c+d =
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.
Define the linear transformation T by T(X) = Ax. 1 -1 3 A = 0 1 3 1. (a) Find the kernel of T. (If there are an infinite number of solutions use t as your parameter.) ker(T) = (b) Find the range of T. {(-t, t): t is any real number} O R² O {(t, 3t): t is any real number} R {(3t, t): t is any real number}
(1 point) If T:R? → R is a linear transformation such that -0-0-0-0-0-0) then