Question

1. Let W be the set of all [x y z}^t in R^3 such that xyz = 0. Is W a subspace of R^3?

2. Let C^0 (R) denote the space of all continuous real-valued functions f(x) of x in R. Let W be the set of all continuous functions f(x) such that f(1) = 0. Is W a subspace of C^0(R)?

Answer #1

**(1)**

**(2)**

1)T F: All (x, y, z) ∈ R 3 with x = y + z is a subspace of R 3
9
2) T F: All (x, y, z) ∈ R 3 with x + z = 2018 is a subspace of R
3
3) T F: All 2 × 2 symmetric matrices is a subspace of M22. (Here
M22 is the vector space of all 2 × 2 matrices.)
4) T F: All polynomials of degree exactly 3 is...

Let W = {(x, y, z, w) ∈ R 4 | x − z = 0 and y + 2z = 0}
(a) Find a basis for W.
(b) Apply the Gram-Schmidt algorithm to find an orthogonal basis
for the subspace (2) U = Span{(1, 0, 1, 0),(1, 1, 0, 0),(0, 1, 0,
1)}.

Consider the following subset:
W =(x, y, z) ∈ R^3; z = 2x - y from R^3.
Of the following statements, only one is true. Which?
(1) W is not a subspace of R^3
(2) W is a subspace of R^3
and {(1, 0, 2), (0, 1, −1)} is a base of W
(3) W is a subspace of R^3
and {(1, 0, 2), (1, 1, −3)} is a base of W
(4) W is a subspace of R^3
and...

Let (X, d) be a metric space, and let U denote the set of all
uniformly continuous functions from X into R. (a) If f,g ∈ U and we
define (f + g) : X → R by (f + g)(x) = f(x) + g(x) for all x in X,
show that f+g∈U. In words,U is a vector space over R. (b)If f,g∈U
and we define (fg) : X → R by (fg)(x) = f(x)g(x) for all x in X,...

Is the set of all x, y, z such x+ 3y + 2z = 0 a subspace of R^3
? If so find a basis for the space.

Prove that the set S = {(x, y, z) ∈ R 3 : x + y + z = b}. is a
subspace of R 3 if and only if b = 0.

Let W be the subset of R^R consisting of all functions of the
form x ?→a · cos(x − b), for real numbers a and b. Show that W is a
subspace of R^R and find its dimension.

1.) Let f ( x , y , z ) = x ^3 + y + z + sin ( x + z ) + e^( x
− y). Determine the line integral of f ( x , y , z ) with respect
to arc length over the line segment from (1, 0, 1) to (2, -1,
0)
2.) Letf ( x , y , z ) = x ^3 * y ^2 + y ^3 * z^...

a. Let →u = (x, y, z) ∈ R^3 and define T : R^3 → R^3 as
T( →u ) = T(x, y, z) = (x + y, 2z − y, x − z)
Find the standard matrix for T and decide whether the map T is
invertible.
If yes then find the inverse transformation, if no, then explain
why.
b. Let (x, y, z) ∈ R^3 be given T : R^3 → R^2 by T(x, y, z) = (x...

Show the vectors [x y z] where xyz=0 is a subspace V of R^3. is it
closed under additon? is it closed under scalar
multiplication?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 8 minutes ago

asked 8 minutes ago

asked 31 minutes ago

asked 40 minutes ago

asked 50 minutes ago

asked 51 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago