Which of the following sets are subspaces of R³: W1 = {(x1, x2, X3) : x3 = 2x1 – 4x2}; W2 = {(x1,X2, X3) : x1 = W3 = {(x1, 2, X3) : x = x1 – 23}; 2.x3 – 2}; = x1 – x3};

Q: The subset in the form where x and y are real numbers, is a subspace of R2 if Select one: O x + 0…

A:

Q: 3. Let W = M2x2(C) with zero determinant. Show that W is not a subspace of V = M2x2(C).

A:

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: If V = W1 ⊕ W2 and W is any subspace of V such that W1 ⊆ W , show that W = W ∩ W1 ⊕ W ∩ W2.

A:

Q: Which of the subsets of R3 is a subspace of R3? (a) W = {(x1, x2, x3): x1 + x2 + x3 = 0} (b) W =…

A: Given:

Q: 3. Determine whether X1 W E R? : x² + x2 = | X2 is a subspace of R².

A:

Q: Determine whether the following sets form subspaces of R3: {(x1, x2, x3)T | x1 = x2 = x3}

A:

Q: Determine whether the following sets form subspaces of R2: {(x1, x2)T | x1 = 3x2}

A:

Q: Why is this set not a subspace of R^3? W = { (a1, a2, a3) : a22 = a1 - a3 } ( the two 2s are…

A:

Q: 3. State why W = {x = (x1, 2, X3, T4) E R' : a1 + x2 + x3 + a4 < 1} is not a subspace of R. (H.W)

A:

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

A:

Q: 2.14. Prove that two subspaces V1 and V2 are linearly independent if and only if Vịn V2 = {0}.

A: V1 and V2 are two subspace.

Q: Q;:Is W={A€ M3(R): a11+a22+a33=1} a subspace of M3(R)?.

A: Note :- A subset S of a vector space is said to be subspace iff  1.S is closed under vector addition…

Q: 3. Let W be the subspace of R3 [x] spanned by the polynomials 1+2x+3x²+4x³, 2+3x+4x²+x³, 3+4x + x² +…

A: Please see the below picture for detailed solution.

Q: Determine whether the following sets form subspaces of R2: {(x1, x2)T | |x1| = |x2|}

A: Subspace means a space whose elements are contained wholly in other space.

Q: Q3 shew that W2 = subspace of R2 is a

A: To show any subset of vector space is a subspace , prove the following condition : Set is closed…

Q: E M2x3 is a subspace of M3-

A:

Q: Determine whether the following sets form subspaces of R2: {(x1, x2)T | x1x2 = 0}

A: Consider the equation:

Q: Determine whether the following are subspaces of C[−1, 1]: The set of odd functions in C[−1, 1]

A: Consider the given set: C[−1, 1] Here the objective is to prove that the set of odd functions in…

Q: 3: Determine whether the following subsets are subspaces a) H = { ||zy = 0} CR". b) H = { x+ 2y + 3z…

A: We have to find

Q: 7. Let W span{x} be a subspace of P2(R) with (p(x), q(x)) = p(x)q(x) dx. Find W-.

A: I am solving this in step 2

Q: Show that H= {p € P3: p(0)+p(1) = 0} is a subspace of P3. %3D

A:

Q: [M] Show that w is in the subspace of R4 spanned by V1, V2, V3, Where 9. -4 -7 -4 -4 3 V3 = V2 = -4…

A:

Q: For each subset W of R² either prove W is a subspace of R² or explain why it is not a subspace. (a)…

A:

Q: find all the 2-dimensional subspaces of GF(3)3.

A:

Q: If W is a subspace, then ||projwv||² + ||v – projwv||2 = ||v|?.

A: Given W is a subspace of a vector space V. Now projWv denotes the projection of vector v onto the…

Q: Determine if v is in the subspace of P3 given by span{x + x - 5, x2 + 2x + 1, x-x2 + x}. v = x? + 2x…

A:

Q: Which of the following subsets of RX3 are subspaces of R³x3

A:

Q: 3 Find a basis of the subspace of R’ defined by the equation -5x1 – 7x2 – 2x3 = 0.

A: Consider the given equation:

Q: Determine whether the following subset S of R³ is a subspace or not. a) S= 3|X2||x1x2x3 = X3 S - b)…

A:

Q: Explain why the subset а —b S : a + b а,b€ R -2b — За of R³ is or is not a subspace of R³.

A:

Q: 3. Let W be the subspace of R3 [x] spanned by the polynomials 1+2x+3x²+4x³, 2+3x+4x²+x³, 3+ 4x + x²…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: In R3, given 2 subspaces V =, V½ = {(x1; X2; X3) E R3|Xı – x2 + mx3 = 0} %3D Find m such that V1 =…

A:

Q: Determine whether W = {ao + a1x + a2x² + a3x°|ao + a2 = az ɑ1} is a subspace of P3.

A:

Q: Which of the following sets are subspaces of R3: W1 = {(x1, x2, x3): x3 = 2x1 – 4.x2}; W2 = {(x1,…

A: A set W, is a subspace of a vector space ℝn if it satisfies the following three properties.  0 is…

Q: If W₁ and W₂ are subspaces of V and dim W₁ (a) W₁ = W₂. (c) W₂ C W₁. dim W2, then (b) W₁ C W₂. (d)…

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

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

A:

Q: Prove that p2 is a subspace of p3.

A:

Q: 14) Find all values of h such that y will be in the subspace of 3 spanned by v1, v2, v3 if vị = 2,…

A:

Q: 3. Consider V = {a2x² +a1x + ao € P2(R) : a2 + a1 + ao = 0} . Use the subspace theorem to show that…

A:

Q: 2. Determine whether the following subset S of R3 is a subspace or not. a) S = X2||x1x2x3 = X3 S.…

A: Let V be a vector space over field F. Let W be a subset of V then W is subspace of V over field F if…

Q: Which of the subsets of R* is a subspace of R³? (a) W = {(x1, x2, X3): x} + x3 + x} = 0} (b) W =…

A: Which of the subsets of R3 is a subspace of R3 ?

Q: Which of the following sets are vector subspaces of R3 and why? i. S1 ={x in R3: x1 + x2 = 0, x1 +…

A: To determine the set S is a subspace if w1 , w2∈S then c1w1+c2w2∈S (i) Consider…

Q: Determine whether the following sets form subspaces of R3: {(x1, x2, x3)T | x1 + x3 = 1}

A: To determine: The set{ x1, x2, x3 such that x1+x3=1} is a subspace of R3or not.

Q: 2. Determine whether W is a subspace of V = C³ where W = {(0,b, c) E C³}. %3D

A:

Q: (c) {(x1, x2, X3)" | x3 = x1 + x2}

A: Set s is subspace of R3

Q: H is not a subspace of R.

A:

Q: L: R3 → R² and L(x) = (2x1 – x2, X2 + x3). Show that ker(L) is a subspace of R3

A:

Q: Determine whether the following sets form subspaces of R2: {(x1, x2)T | x2/1= x2/2}

A: Consider the given sets. Find if the condition satisfies for x1 =1 and x2 = 1.…

Q: For each of the following subsets of R", determine whether it is a subspace of R" or not a) S =…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.