HW10P5 (10 points) Let A be the matrix A =13 5 0 (3 pts) Find the elementary matrices that perform the following row operations in sequence: a. 21 * 2 2. E31 : R3 R1R3 b. (3 pts) Show that the elementary matrices you found in (a) can be used as elimination matrices to determine the upper triangular, U, matrix of A. (4 pts) Find the lower triangular, L, matrix that verifies A C. = LU.
6, (6 pts.) Let > 0 be a constant. Show that the random variable X with probability density function f(x) = 0 If x < 0. "has no memory." More precisely, show that P(X > t|X > s} = P(X > t-s) for any 0 s t< oo.
HW10P5 (10 points) 3 2 -1 Let A be the matrix A = 1-3 0 6 -2 1 a. (4 pts) Find the multipliers l21, 131,132 and the elemention matrices E21, E31, E32 b. (2 pts) Use the multipliers l21, 131,132 to construct the lower triangular matrix, L c. (2 pts) Use the elimination matrices to determine the upper triangular, U, matrix of A d. (2 pts) verify that LU A
b) (10 pts) Let D(0, oo)) be the vector space of all bounded continuous functions from [0, oo) such that R If(x) dz 00. Give an example of a sequence {fn} of functions in D(0,00)) which (i) converges pointwise for E [0, oo) to the constant function f(z)0 (ii) does not converge to 0, neither with respect to the norm, nor the Hint: it may be helpful to contemplate the phrase "mass escaping to infinity". norm. b) (10 pts) Let...
1. (50 pts.) Let A be the 3 x 3 matrix A= 0 0 3 0 2 0 3 0 0 :) i. Compute the eigenvectors ū1, U2, U3 of A. ii. Verify that the matrix S with columns ū ū2, öz has full rank. iii. Use the Gram-Schmidt process to change B into an orthogonal matrix P.
Please answer this using matrices quick thanks 1. Let A be a 3 x 3 matrix with det (A) 4, and suppose the matrix B is obtained from A by performing the following elementary row/column operations to A: -a Ra+ Rs For what value(s) of a does det(B)-6?
4.(5 pts)Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is diagonalizable. Show that it is, in fact, diagonalizable, and find C and D such that C (you may make this as trivial as you wish!) AC = D 5.(5 pts) Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is NOT diagonalizable. Show WHY it is not diagonalizable. 6. (5 pts) Let T:...
6. Let S : R + R3 be the linear transformation which satisfies |(1,0,0) = (1,0,–3), S(0,1,0) = (0,-1,0) and S(0,0,1) = (1,-1, -2). Give an expression for S(x, y, z). 4 Marks] Let S be the basis (1,0,0), (0,1,0), (0,0,1) for R3 and let T be the basis (0,0,1), (0,1,1), (1,1,1) for R. Compute the change of basis matrix s[1]7. (b) Compute the matrices s[S]s and s[ST. 18 Marks)
How can I get the (a) 3*2 matrix A? x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0 y (a) Find a 3x2 matrix A whose column space is V and the entries a a1 0 = (b) Find an orthonormal basis for V by applying the Gram-Schmidt procedure (c) Find the projection matrix P projecting onto the left nullspace (not the column space) of A (d) Find an SVD (A...
Chapter 8, Section 8.5, Question 07 x Incorrect Find the matrix of T with respect to the basis B, and use Theorem 8.5.2 to compute the matrix of T with respect to the basis B . T:R2 R2 is defined by X1- 2x2 X1 T X2 -X2 B = u1, u2} and B = {v1, V2}, where 2 1 V1 = u2 = 1 1 Give exact answer. Write the elements of the matrix in the form of a simple...