which of the following are subspaces of MNXN

Q: 4. The set W of polynomials of the form a² + α₁x + α₂x² + 3x³ + α4x4, where a₁ = a₂ and a₁ = az is a…

A: 4. Given that the set W is of the polynomials a0+a1 x+a2 x2+a3 x3+a4 x4 where a0=a2 and a1=a3 is a…

Q: Find the orthogonal projection of 9. -3 = 4 onto the subspace W of Rª spanned by -3 -4 3 and 6 -3…

A: Solution:-

Q: Determine whether the set S spans R3. If the set does not span R3, then give a geometric description…

A:

Q: basis for each of the following subspace of R³

A:

Q: If S and T are subspaces of V, then SintersectionT is a subspace. Select one: True False

A: A detailed solution is given below.

Q: One of the following subsets of R² is not subspace. Select one: а. X1 S={ X1=2x2} b. S={ ,X1 =X2} C.…

A: We will check that which subset is not a subspace of R2

Q: The set of all polynomials of the form ax³ bx² cx + 2, where a,b and can real numbers is a subspace…

A:

Q: Q3 Give an example of a connected subspace of R2 which is not path- connected.

A:

Q: If y is in a subspace W, then y - ŷ is not zero. Select one: O True False

A: Solve the following

Q: Suppose U and W are subspaces of V for which UUW is a subspace. Show that UCW or WCU.

A:

Q: Give an example of a subset (not subspace) of R3 that has an infinite number of elements, is closed…

A: A subset W of vector space V over the scalar field K is a subspace of V if and only if following…

Q: Which of the following subsets of R3x3 are subspaces of R³×3?

A:

Q: cide, with justification if the following subsets of R* are in fact subspaces of R*: ) V b2 with b…

A:

Q: Determine a basis and the dimension of the following subspace of R4. V = span((1, – 1,2, 4)", (1, 1,…

A:

Q: Determine whether the set S spans R3. If the set does not span R3, then give a geometric description…

A:

Q: Show that H = : a, b eR is a subspace of M2x2(R). Hint: try to write H as the spa of a set of…

A:

Q: Determine if all polynomials P = ao + a,x + a,x² + a3x³ , with ao, a1, a2, az integer, is subspace…

A:

Q: 11. Explain why the subset of R² shaded below is not a subspace of R². 3 1 -3 -2 -1 -1 -2 -3 12.…

A: I have given the details below

Q: 7. The set of all 2 × 2 upper triangular matrices is a subspace of M2,2 . a. True. b. False.

A:

Q: Determine if the given subset is a subspace of R^3

A:

Q: Find a basis for the subspace of R* spanned by S. S = {(-11, -6, -4, -8), (-6, -3, -2, -4), (4, 2,…

A:

Q: which of the following are subspaces of R3

A: Any subspace of R3  must allow the three coordinates to occupy values along R    in (c) , it is…

Q: 3 1 Show that the null space of A is a 02 subspace of R³. Which subspace can you obtain by the…

A: It is given that,  A = 13-1024 We have to show that the null space of A is a subspace of ℝ3 and to…

Q: Determine whether the following are subspaces of P4 (be careful!): The set of polynomials in P4 of…

A:

Q: Identify which of the following sets are open in [-1, 2) as a subspace of R. - (0, 2) [1, 2) [-1, 0]…

A: Open Sets: The sets in τ are called the open sets of the topological space X, τ. Subspace Topology:…

Q: Let S be a 2D subspace of R. Find projs if projs =

A: Let S is a 2D subspace of ℝ3 projs<2,-1,1>=<0.5,0.5,1> So consider the 2-D plane given…

Q: 10 Find the projection of 69 -15 -4 subspace W of R³ spanned by -6 and - 14 onto the √] 6 -

A: Given v→=10-14-15 The objective is to find the projW(v→).

Q: If S and T are subspaces of V, then sNT is a subspace. Select one: O True False

A: Question 1) true  Q. If S and T are subspaces of  a  vector space VTo prove: S∩T is a subspace of…

Q: very vector of subspace W5 is orthogonal to each vector in subspace V5.

A:

Q: ate be two Subspaces fram Rs ver Ehe field IR Final wiAWe

A: Answer

Q: Give an example of a two-dimensional subspace of P3.

A: To give an example of a two - dimensional subspace of P3.   Definitions:             Let V be…

Q: 4. Which of the following sets are subspace of Mmxn? (a) The set of all 2 x 3 matrices of the form b…

A:

Q: Check which of the subsets below are M2x2 subspaces with operations usual. (a) The set of all 2 x…

A:

Q: Q4. Check the following set is a subspace of R3 or not U = ((x1, x2,x3)| x, = v2 x} %3D

A: The given subset of ℝ3 is: U=x1, x2, x3 |x2=2x1 Definition: Let W be a subset of the vector space V.…

Q: = { (; ):a,b eR }with the standard operations in M22. Let W Which of the following statements is…

A: Lets solve the question

Q: Find the orthogonal projection of -19 5 -5 -12 onto the subspace W of IRª spanned by 1 -4 and 5 10

A: As per the orthogonal Decomposition  theorem  Let us assume W is a subspace of Rn then each y in Rn…

Q: A) The set of all ax³ - bx² - Select one: O True O False polynomials of the form cx + 2, where a,b…

A:

Q: Which of the following subsets of R3x3 are subspaces of Rx3? OA. The diagonal 3 x 3 matrices OB. The…

A:

Q: Determine all subspaces of W.

A:

Q: 8) Describe geometrically all subspaces of R" for n 1, 2, 3.

A: We will do this for all three parts; n = 1, 2, and 3 (in as clear handwriting as possible)

Q: Show that the set of all polynomials of degree at most 3 forms a subspace of Pn.

A:

Q: Which of the following subsets of R³×³ are subspaces of R³×³? A. The 3 x 3 matrices whose entries…

A: The diagonal 3×3 matrices is subspace of R3×3

Q: Find a linearly independent collection of vectors which spans the following subspace of R4: 2 3 -3…

A:

Q: Select one: O a. a subspace of M_2x2 with dimensic O b. a subspace of M_2x2 with dimensio O c. not a…

A: a) Given set is W=a-b-aa; a,b ∈R This shows that W is a non-empty subset of M2×2

Q: 15. Let S = span be a subspace of M2. Is A = 4 in S? If so, write A as a linear combination of the…

A:

Q: Check which of the subsets below are M2x2 subspaces with operations usual.   (a) The set of all…

A:

Q: Determine the dimension of the subspace H, where H = -6

A:

Q: Suppose p1, p2,p3, p4 are specific polynomials that span a two-dimensional subspace H of p5.…

A: