8. Let T: RR be the function T(x) = mx +b, where m and b are some constants. Prove that T is a linear transformation if and only if b = 0.
8. Let T: R+R be the function T(x) = mx +b, where m and b are some constants. Prove that T is a linear transformation if and only if b = 0.
8. Let T: R → R be the function T(x) = mx + b, where m and b are some constants. Prove that T is a linear transformation if and only if b = 0.
= mx + b, where m and b are some constants. Prove that T is a linear 8. Let T: R → R be the function T(x) transformation if and only if b = 0.
Question 28 Condition for the Question : Please solve it according to Introduction to Linear Algebra, so do not use any other concepts from advanced Linear algebra. make sure to double check your answer to get a full credit. Let T:R → R be the function T(x) = mx + b, where m and b are some constants. Prove that T is a linear transformation if and only if b = 0.
12. let Mx(1) be the moment generating function of X. Show that (a) Mex+o(t) = eMx(at). (b) TX - Normal(), o?) and moment generating function of X is Mx (0) - to'p. Show that the random variable 2 - Normal(0,1) 13. IX. X X . are mutually independent normal random variables with means t o ... and variances o, o,...,0, then prove that X NOEL ?). 14. If Mx(1) be the moment generating function of X. Show that (a) log(Mx...
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.
7.) 10points Let V be the space of 2 x 2 matrices. Let T: V-V be given by T(A) = A a.) Prove that T a linear transformation b.) Find a basis for the nullspace (Kernel) of T. c) Find a basis for the range of T.
7.) 10points Let V be the space of 2 x 2 matrices. Let T: V-V be given by T(A) = A a.) Prove that T a linear transformation b.) Find a basis for...
3. Let X be a random variable and denote by Mx(t) its MGF. Prove that, for any t > 0, we have
3. Let X be a random variable and denote by Mx(t) its MGF. Prove that, for any t > 0, we have
Function X AX Where X abx? - abot toa-d, where Determine Wheller linear transformation. T: R2 T: Main Mmm T (A) = IS Fixed matric R. T (A)=lxal, where to Mon is fixed matrisc IR T (x, y) = (x-y, Ory) A=fa b d T: P₂ - Mand T Caxc² + box + = [a-b be a-c T: P - P. , T (ax² + bx tc) = abcx + Carb+c) x