Consider the following subspaces of P. H = Span{1+t, 1 – t³} and G = Span{1+t+t?, t – t³, 1+ t+ t³} Find dim H, dim G and dim HNG.

Q: 3. Determine whether the given set is a subspace of M2x2 with real entries. {6 ) la = b}.

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Q: Consider the following subspaces of P. H = Span{1 + t, 1 − t 3 } and G = Span{1 + t + t 2 , t − t 3…

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Q: Show that W = {(x1, x2): x1 ≥ 0 and x2 ≥ 0}, with the standard operations, is not a subspace of R2.

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Q: Consider the subspace V of R4 given by 1 3 1 V = span || -1 1 1

A: Solution:-

Q: Let W = {a + bx + cx2| a+b >1} with the standard operations in P2. Which of the following statements…

A: Given set is

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

A:

Q: Let W = {a + bx + x2 E P: a, b ER} with the standard operations in P2. Which of the following…

A: W is a subspace of a vector space V

Q: Find the intersection of the following two affine subspaces of R4. 1 1 0 1 1 1 1 1 0 0 1 y 1 1

A: Let's find.

Q: Determine: If W = the set of all vectors in R2 whose second component is the square of the first. is…

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Q: Consider the following subspaces of P. H = Span{1 + t , 1 - t3} and G = Span{1 + t + t2, t - t3 ,1 +…

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Q: Let vị 2,v2 8,and w Determine if w is in the subspace of R generated by v1 and v2.

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Q: Prove that W1 = {(a,b) E R² : 4a – b= 0} is a subspace of R2.

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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: 1. Determine whether w - {[:]•r:a-4-0} X1 E R? : : x1 – 23 = X2 is a subspace of R?.

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Q: 4. Consider the following subspaces of P. H = Span{1+t, 1– t°} and G= Span{1+t+t°, t – t°, 1+t+t}…

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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: 4. Consider the following subspaces of P. H = Span{1+t, 1-t3 } and G = Span{1+t+t 2, t – t 3, 1+t+t…

A:

Q: What is the dimension of the following subspace U of R2x2 ? 3 U = span({ }) -2 -2

A:

Q: Let W1 and W2 be subspaces of a finite-dimensional vector space V. Determine necessary and…

A: Consider W1 and W2 be the subspaces of finite dimensional vector spaces V.

Q: 1. Determine whether W ER is a subspace of M. %3D b 2a

A: We have to determine whether W is a subspace of M22.   According top our guidelines we can solve…

Q: 4. Consider the following subspaces of P. H = Span{1+t, 1– t°} and G=Span{1+t+t°, t – t°, 1+ t+t®}…

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Q: Show that the set T= {(a, b, c, d): 2a-3b+Sc-d=0} is a subspace of R'.

A: Given T=abcd∈ℝ4:2a-3b+5c-d=0 Let A be a 1×4 matrix defined by: A=2-35-1 Then the equation…

Q: Show that S is a subspace of R2 where S = {x € R²: x=(5k, 10k), k = R}.

A: Given  S = x∈ℝ2 : x=5k, 10k, k∈ℝ. We have to show that S is a subspace of ℝ2.

Q: Consider the following subspaces of P. H = Span{1 +t ,  1 - t3} and G = Span{1 + t + t2,  t - t3,  1…

A:

Q: Show that W = {a + bx² € P₂|a, b = R} is a subspace of P2.

A: The solution is given as

Q: Determine whether W = {(a,2,b)la, b ER} is a subspace of R³.

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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…

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Q: Let W1 and W2 be subspaces of a vector space V over K, and let S1 be a subset of Wı and S2 a subset…

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: The set {(x,3): x is in R)} is a subspace of R2

A: The given set is x,3: x is in R. It is known that any subspace should contain identity element.

Q: i) Determine whether the set W = {(x1, x2, x1x2) : xị and r2 are real numbers} is a subspace of R³…

A: Introduction: We prove the given set to be valid as per the standard conditions:

Q: Explain why the subset а — b S = a +b а,bER -26 – 3a of R3 is or is not a subspace of R³.

A: Given subset of R3 is  S={a-ba+b-2b-3a|a,b∈R} explain if S is subspace of R3

Q: Show that the set W = {(x1, 0, x3): x1 and x3 are real numbers} is a subspace of R3 with the…

A: Given: the set W = {(x1, 0, x3): x1 and x3 are real numbers} is a subspace of R3 with the standard…

Q: 2. Determine which of the following is a subspace of R". (a) {(x1,x2,...X) 1 x = 0} (b) {(x1,…

A:

Q: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R b)show that R° = F1…

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Q: Show that S = {(a,0, b)"|a,b E R} forms a subspace of R³.

A: The solution are next step

Q: Consider the following subspaces of P. H = Span{1 + t, 1 − t3} and G = Span{1 + t + t2 , t − t3 , 1…

A:

Q: Let vi # v2 E R" and define W1 Span{v2}. Use the definition to show W+n W, is a subspace of R".…

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: 5. Let P2 be the vector space of polynomials of degree at most 2. Determine if the vector v = = 10x…

A: Consider the given vector v is in the given subspace. Consider the real numbers a, b such that the…

Q: H is not a subspace of R.

A:

Q: Find all values of h such that y will be in the subspace of R³ spanned 3] by v1, V2, V3 if v1 =| 2|,…

A:

Q: Let W1 and W2 be subspaces of a vector space V. Prove that W1 ∪W2 is a subspace of V if and only if…

A: It is given that W1 and W2 are the two subspaces of the vector space V.

Q: Look for or create your own set W that is a subspace of R' or R.

A: We create a subspace of ℝ3.

Q: Find a basis and the dimension of the subspace W = {(a+1)x+(2-b)x²; a,b e R} of P,.

A:

Q: Find the intersection of the following two affine subspaces of R4. 1 1 0 1 1 1 1 1 0 0 1 y 1 1 w

A: Topic:- matrix

Q: Let W, and W2 be subspaces of a finite-dimensional vector space V. Determine necessary and…

A: Given that  W1  and W2 are the sub spaces of a finite dimensional vector space V.

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.