suppose that T:R^3 →R^2 is such that
T(e1)= [ 2] T(e2)= [ 1 ] T(e3)=[ 0 ]
[ 1 ] [ 1 ] [ 1]
and suppose that S : R^2 → R ^2 is given by the projection onto the x axis
(a) What is the matrix S◦ T?
(b) What is the kernel of S◦T?
suppose that T:R^3 →R^2 is such that T(e1)= [ 2] T(e2)= [ 1 ] T(e3)=[ 0...
Let S be the tetrahedron in R3 with vertices at x the vectors 0, e1, e2, and e3, and let S' be the tetrahedron with vertices at vectors 0, v1, V2 and v3. See the figures to the right. Complete parts (a) and (b) below. a. Describe a linear transformation that maps S onto S lf T is a linear transformation that maps S onto S, then the standard matrix for T, written in terms of v1-v2, and v3, is...
2. Consider matrix A = 5 0 1 2 Find elementary matrices E1, E2 and E3 such that E3E2E1A=I.
F is an event, and E1, E2, and E3 partition S. P(E1) = 5 12 , P(E2) = 4 12 , P(E3) = 3 12 P(F | E1) = 2 5 , P(F | E2) = 1 4 , P(F | E3) = 1 3 Draw the tree diagram that represents the given information. (a) Find P(E1 ∩ F), P(E2 ∩ F), P(E3 ∩ F). P(E1 ∩ F) = P(E2 ∩ F) = P(E3 ∩ F) = (b) Find P(F). P(F) =...
Find the inverse of the elementary matrix E1 E2 E3 E4 and show the step 1 2 3 4
suppose that we have a sample space s={E1,E2,E3,E4,E5,E6,E7}, where E1 to E7 denote the sample points. The following probability assignments apply: p(E1 )=.05 p(E2)=.20 P(E3)=.20 p(E4)=.25 p(E5)=.15 p(E6)=.10 and p(E7)=.05 Let A={E1,E4,E6} B={E2,E4,E7} C= {E2,E3,E5,E7} 1) Find A ∩ B and P(A ∩ B) and Are events A and C mutually exclusive?
Suppose a sample space consists of five elementary outcomes e1, e2, e3, e4, e5with the characteristics that e1, e4, and e5are equally likely, e2is twice as likely ase1and e3is four times as likely as e1. a. DetermineP(ei) for i = 1, 2, ... 5 b. IfA = {e3, e4}, find P( A ).
Recall that if T: R" R" is a linear transforrmation T(x) = [Tx, where [T is the transformation matrix, then 1. ker(T) null([T] (ker(T) is the kernel of T) 2. T is one-to-one exactly when ker(T) = {0 3. range of T subspace spanned by the columns of [T] col([T) 4. T is onto exactly when T(x) = [Tx = b is consistent for all b in R". 5. Also, T is onto exactly when range of T col([T]) =...
Suppose that T:R? + R2 is linear, T an .What Suppose thatT: R + P?is linear, 1 (1) = ( 1 ) and T ( 1) = (3) what ist(3)? • (1) ° (6) None of the others
(c) [1 point] Let R : E3 → E3 be the rotation in E3 with axis in the direction of the vector ã=(-1,2, -2) and angle 0 = . If pe E3 denotes the point (0,0,1) then ... R(p) = (d) [1 point] Let R: E2 → Eº be a reflection through a line l that fixes the origin and sends (1,1) to some point on the line y = x. Can you determine the line l? If so, give...
Problem 2. Recall that for any subspace V of R", the orthogonal projection onto V is the map projy : RM → Rn given by projy() = il for all i ER", where Ill is the unique element in V such that i-le Vt. For any vector space W, a linear transformation T: W W is called a projection if ToT=T. In each of (a) - (d) below, determine whether the given statement regarding projections is true or false, and...