[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 -3 -2 -5 9. -8 -18

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

A:

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: Show that the set W : {(x, y, 5x-4y)| x and y are real numbers} is a subspace of R³.

A: We are give, W=x,y,5x-4y| x and y are real numbers To show: W is a subspace of R3 This can be done…

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: 4) Show that the subspaces of R? are precisely {0}, R2, and all lines in R? through the origin.

A: A subspace of a vector space is itself a vector space that is contained in another vector space.

Q: Prove that every line through the origin in R3 is a subspace of R3.

A: To prove that every line through the origin in R3 is a subspace of R3.

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

A: Solution:-

Q: Find the closest point to y in the subspace W spanned by v, and v2. 13 1 5 - 1 y = 1 1 , V2 = 1 - 1…

A: Given y=13-112,v1=11-1-2,v2=5103. The orthogonal projection of y onto span of v1, v2 is…

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

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Q: Determine whether the following are subspaces of C[−1, 1]: The set of continuous nondecreasing…

A: According to the given information,

Q: Q4(a) Define the null space of an m x n matrix A and prove that it is a subspace of R"

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Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw (v) |||| 6 V H 14 2 and…

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Q: (c) Find a subspace U such that R³ = W₁ OU.

A: C. Hint: Use the result of part (b) in the part (c) and obtain the required result.

Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 -1 -1 projw (7) = %3|

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Q: What is the dimension of the subspace of P4 consisting of all polynomials p(x) such that p(0) =2p(1)…

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Q: can a subspace of R^n have a dimension less than n.

A: Yes , it can be .

Q: Find the closest point to y in the subspace W spanned by v1 and v2 1 ,V2 = 1 y = V1 = -3. I • E 2 b)…

A: Here we have to find the closest point to y in the subspace W spanned by v1 and v2 .

Q: 10. Under the usual operations in R2, which of the following subsets is a subspace? (a) y = 2ar…

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Q: 2. Let P3(R) be the vector space of all polynomials of degree 3 or less (and the zero polynomial).…

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

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Q: If Sz is a subspace of R" of dimension 3, then there cannot exist a subspace S, of R* such that Si c…

A: This staement is true.

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: b.) show that IR³ - W₁ + W₂. t C.) Find a subspace V such that IR³ =W₁ U.

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

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Q: Verify that W is a subspace of V. In each case, assume that V has the standard operations.{(x, y, 4x…

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Q: Show that if W₁ and W₂ are subspaces, then W₁ U W₂ is not a subspace unless one is a subspace of the…

A: We have to prove that if W1 and W2 are subspaces, then W1∪W2 is not a subspace unless one is a…

Q: Let Pn be the set of real polynomials of degree at most n. Show that is a subspace of P6- S = {p €…

A:

Q: If Sz is a subspace of R* of dimension 3, then there cannot exist a subspace S2 of R* such that S, c…

A: S1, S2 are subspaces of R4 such that S1⊂S2⊂R4 with S1≠S2 and S2≠R4.

Q: What is the dimension of w = {A € M2x2 (R) : A"| =ö} ĄT -2 1 2 This is not a subspace

A: W=AEM2×2(R) : AT1-2=→0  Let A=abcd, a,b,c,dER     AT=acbd     AT1-2=→0  ⇒acbd 1-2 =00 ⇒a-2cb-2d=00…

Q: Find the closest point to y in the subspace W spanned by vị and vz 2 y =| 1 ,v1 0,v2 -2 2 а) b) c)…

A: The following is the solved answer.

Q: Is M = {(x,y,z)|x is nonnegative} a subspace of R³? Yes or No? Justify or give/find a…

A: Given  M =  x, y, z  x is nonnegative

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: 4. Show/prove whether the following is a subspace. 1 {x € R3:x =| 3| +s 2+t1,for s,t e R}

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Q: 4) Find all values of h such that Y will be in the subspace of 3. R spanned by VI) V2, V3 if V I V2…

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Q: -2 , find the closest point to v in the subspace W spanned by -2 Given v =

A: Introduction: Th formula for the projection of vector w on v is given by,…

Q: [M] Determine if y is in the subspace of R4 spanned by the columns of A, where -4 3 -5 -9 -8 7 -6 y…

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Q: 1- Show whether the set of polynomials a, +at +at+at ,where a, =a, +a, is a subspace of P3 or not ?

A: Let V be a vector space over the field F. A non-empty subset S of the vector space V is said to be a…

Q: Find the orthogonal projection of -13] 15 onto the subspace W of R4 spanned by 4 and 5 -2 -2…

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Q: Determine whether W is a subspace of V

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Q: Find the orthogonal projection of [-10] = -15 12 onto the subspace W of IR spanned by 日-日 1 9. and 6…

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Q: Find the dimension of the subspace W of R4 spanned by S = {v1, v2, v3} = {(−1, 2, 5, 0), (3, 0, 1,…

A: Dimension of a subspace W is given by the number of linearly independent vectors in the basis of W,…

Q: 10. Find the dimension of the subspace V span{v1, v2, V3, v4} in R³ where vi 1 V2 = , V3 = and v4 =

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

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Q: Which of the following are subspaces of R°?

A: PART - A- Concept Used: W is said to be subspace of the vector space V if W≠∅…

Q: 2 Find the dimension of the subspace H of R spanned by – 12 8 ..... dim H =

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Q: Show that points on the plane x-2y+4z=0 form a subspace of R3

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

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Q: Q2. Check if the following points lies on the subspace U spanned by the vectors = [2 -1 2]', x2 = [0…

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