Determine whether the set together with the standard operations is a subspace of M2,2. Justify the answer:
Determine whether the set together with the standard operations is a subspace of M2,2. Justify the...
Determine whether the set w is a subspace of R3 with the standard operations. If not, state why. (Select all that apply.) W = {(x1, 1/X1, X3): X1 and xy are real numbers, X1 + 0) W is a subspace of R W is not a subspace of R because it is not closed under addition. Wis not a subspace of R because it is not closed under scalar multiplication. X
part a and b
PROBLEM (HAND-IN ASSIGNMENT) Use the Subspace Test to determine whether the following sets W are subspaces of the given vector spaces: (A) The set W to be of all triples of real numbers (x, y, z) satisfying that 2x - 3y + 5z = 0 with the standard operations on Ris a subspace of R3. (B) The set of all 2 x 2 invertible matrices with the standard matrix addition and scalar multiplication.
[-/1 Points] DETAILS LARLINALG8 4.3.003. Is W a subspace of V? If not, state why. Assume that has the standard operations. (Select all that apply.) W is the set of all 2 x 2 matrices of the form [1] V = M2,2 W is a subspace of V. W is not a subspace of because it is not closed under addition. W is not a subspace of V because it is not closed under scalar multiplication. Submit Answer Viewing Saved...
(1 point) Determine whether the given set S is a subspace of the vector space V. A. V = R", and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed mxn matrix. B. V is the vector space of all real-valued functions defined on the interval (-oo, oo), and S is the subset of V consisting of those functions satisfying f(0) 0 C. V Mn (R), and S is the...
Determine whether the given set S is a subspace of
the vector space V.A. V=C2(ℝ) (twice continuously
differentiable functions), and S is the subset of VV consisting of
those functions satisfying the differential equation
y″=0. B. V=ℙ5, and SS is the subset of ℙ5 consisting of those polynomials satisfying
p(1)>p(0)C. V=ℙ4, and SS is the subset of ℙ4 consisting of all polynomials of the form
p(x)=ax3+bx.D. V=Mn×n(ℝ), and SS is the subset of all
symmetric matrices.E. V=ℝ2, and S consists of...
linear algebra
1. Determine whether the given set, along with the specified operations of addition and scalar multiplication, is a vector space (over R). If it is not, list all of the axioms that fail to hold. a The set of all vectors in R2 of the form , with the usual vector addition and scalar multiplication b) R2 with the usual scalar multiplication but addition defined by 31+21 y1 y2 c) The set of all positive real numbers, with...
(a) State whether the following statement is true or false. The follow set is a subspace of P2, where P2 is the set of all polynomials over the real numbers of degree 2 or less. W={p € P2 :p (3)=0} O True O Fale In the essay box below, if it is true, prove that W is closed under scalar multiplication. Otherwise, give an explantion why the statement is false. XDX HE Editor A-AIBIU S *** Styles Font Size Words:...
Name: Math 23 6. (14 points) Determine whether the following subsets are subspaces of the given veeto r space. Either prove that the set is a subspace or prove that it is not (a) The subset T C Ps of polynomials of degree less than or equal to 3 that are of the form p(x)-1+iz+o2+caz3, where c,02, c3 are scalars in R. (b) The set s-a a,bERM22, that is, the subset of all 2 x 2 matrices A where a11-a22...
PART 2: Assorted Problems. Show all work for full credit. (8) 1. In each of the following, determine whether or not the subset W of the vector space Vis a subspace of V. Justify your conclusions. a. V-Mn: W the set of all 2x2 matrices with rational number entrics b. VP: W-the set of all polynomials a, +ar+a in where a, +a, -2a, -o. (b) 2. Find elementary matrices E,E, such that EA-B and E,B-A when 2 7 3 8...
I need help with these linear algebra problems. 1. Consider the following subsets of R3. Explain why each is is not a subspace. (a) The points in the xy-plane in the first quadrant. (b) All integer solutions to the equation x2 + y2 = z2 . (c) All points on the line x + z = 5. (d) All vectors where the three coordinates are the same in absolute value. 2. In each of the following, state whether it is...