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2. Consider matrix A = 5 0 1 2 Find elementary matrices E1, E2 and E3...
Find the inverse of the elementary matrix E1 E2 E3 E4 and show the step 1 2 3 4
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 ).
Question 6 1 pts Consider the three energies E1, E2, and E3 (E1> E2>E3). Which shows the largest relative probability? P(E1)/P(E2) P(E1)/P(E3) P(E2P(E1) P(E3)P(E1) P(E3)/P(E2)
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) =...
Given -1 1 A= = 20 0 find elementary matrices E1, ..., Ex such that Ex---E, E, A = 13.
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?
1 3 1. Find the inverse using elementary matrices A 2-3 Find a sequence of elementary matrices whose product is the given matrix. 2-H 4 3 Find an LU-factorization. 3 01 6 1 1 3. -3 1 3 1. Find the inverse using elementary matrices A 2-3 Find a sequence of elementary matrices whose product is the given matrix. 2-H 4 3 Find an LU-factorization. 3 01 6 1 1 3. -3 1
4. Consider the vector space V = R3 and the matrix 2 -1 -1 2 -1 -1 0 2 We can define an inner product on V by (v, w) = v'Mw. where vt indicates the transpose. Please note this is NOT the standard dot product. It is a inner product different (a) (5 points) Apply the Gram-Schmidt process to the basis E = {e1,e2, e3} (the standard basis) to find an orthogonal basis B. 4. Consider the vector space...
1 Let A = (4 22 a) Find elementary matrices E, Er Ez - such that 2 E3 E₂E, A = I b) Find A
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...