Question

In: Advanced Math

consider the subspace W=span[(4,-2,1)^T,(2,0,3)^T,(2,-4,-7)^T] Find A) basis of W B) Dimension of W C) is vector...

consider the subspace W=span[(4,-2,1)^T,(2,0,3)^T,(2,-4,-7)^T]

Find

A) basis of W

B) Dimension of W

C) is vector v=[0,-2,-5]^T contained in W? if yes espress as linear combantion

Solutions

Expert Solution


Related Solutions

Find a basis for the subspace of R4 spanned by (1,0,-2,1), (2,-1,2,1), (1,1,1,1), (0,1,0,1), (0,1,1,0) containing...
Find a basis for the subspace of R4 spanned by (1,0,-2,1), (2,-1,2,1), (1,1,1,1), (0,1,0,1), (0,1,1,0) containing the first and fifth vectors
Find a basis and the dimension of the subspace: V = {(x1, x2, x3, x4)| 2x1...
Find a basis and the dimension of the subspace: V = {(x1, x2, x3, x4)| 2x1 = x2 + x3, x2 − 2x4 = 0}
Find a basis and the dimension of W. Show algebraically how you found your answer. a....
Find a basis and the dimension of W. Show algebraically how you found your answer. a. W = {(x1, x2, x3, x4) ∈ R^4 | x2 = x3 and x1 + x4 = 0} b. W = {( A ∈ M 3x3 (R) | A is an upper triangular matrix} c. W = { f ∈ P3 (R) | f(0) = 0.
Find the value of a : b : c : d, if a : b = 2 : 3, b : c = 4 : 5 and c : d = 6 : 7.
Find the value of a : b : c : d, if a : b = 2 : 3, b : c = 4 : 5 and c : d = 6 : 7.
Consider the triangle which has a=4, b=7 and c=8 Find the measure of angles ∠A=, ∠B=...
Consider the triangle which has a=4, b=7 and c=8 Find the measure of angles ∠A=, ∠B= and ∠C= Give your answer in degrees to at least 3 decimal places.
Find a basis of U = span {(1,1,2,3), (2,4,1,0), (1,5,-4,-9)}
Find a basis of U = span {(1,1,2,3), (2,4,1,0), (1,5,-4,-9)}
V is a subspace of inner-product space R3, generated by vector u =[1 1 2]T and...
V is a subspace of inner-product space R3, generated by vector u =[1 1 2]T and v =[ 2 2 3]T. T is transpose (1) Find its orthogonal complement space V┴ ; (2) Find the dimension of space W = V+ V┴; (3) Find the angle q between u and v; also the angle b between u and normalized x with respect to its 2-norm. (4) Considering v’ = av, a is a scaler, show the angle q’ between u...
(a) Show that the lines r 1 (t) = (2,1,−4) + t(−1,1,−1) and r 2 (s)...
(a) Show that the lines r 1 (t) = (2,1,−4) + t(−1,1,−1) and r 2 (s) = (1,0,0) + s(0,1,−2) are skew. (b) The two lines in (a) lie in parallel planes. Find equations for these two planes. Express your answer in the form ax+by+cz +d = 0. [Hint: The two planes will share a normal vector n. How would one find n?] would one find n?]
A = [4, 5, 9] B = [-4, 5, -7] C = [2, -7, -8, 5]...
A = [4, 5, 9] B = [-4, 5, -7] C = [2, -7, -8, 5] D = [1, -9, 5, -3] E = [3, 3, -1] Uz = 1/|z| ^z d(X,Y) = (Rθ) d = diameter R = Radius θ = Theta Find a. Uc b. d (D, C) c. Let P = B + 3E, UP = d. A x B e. 3B x E f. C x D
Find the matrix A' for T relative to the basis B'. T: R3 → R3, T(x,...
Find the matrix A' for T relative to the basis B'. T: R3 → R3, T(x, y, z) = (y − z, x − z, x − y), B' = {(5, 0, −1), (−3, 2, −1), (4, −6, 5)}
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT