Q. 5 If V is any vector space, show that (0} and V are subspaces of V.

Q: Which of the following is not a subspace of R? Select one: O A. W={X: I1 B W= {X:1= T, of I, = O…

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Q: 2. Determine whether the set W = {(x,y, z)|x + y +z = 0} is a subspace of R3

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Q: Which of the following are subspaces of R^3?  W ={(x, y, z) :x+y+z=0}

A: Given, W=x,y,z:x+y+z=0 Let, 2,-1,1∈W Let, -1∈F

Q: c) Prove that if U and W are subspaces of a vector space V, then their intersection UnW is also a…

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Q: 4. Assume that T E L(V) and that U1 and U2 are T-invariant subspaces of V. Prove that U1 n U2 is…

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Q: What is the dimensionality of the subspace spanned by V = \v +7w for the following v, w? a) b) d) 12

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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: Which of the followings is not a subspace of the vector space V? a) V = Mxn(R),W = {A € VIAT = A} b)…

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Q: The shape's vector set is a subspace of R3

A: solution :-

Q: 6. Let U and W be 3-dimensional subspaces of a 4-dimensional vector space V, and suppose that U # W.…

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Q: Suppose U = {(z, 2, ,9) *:1,y € F}. Find a subspace W of F such that F* = U e W.

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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: Let X =R, and M = (0} , the M is not subspace of R O True O False

A: Subspace of a vector space

Q: Prove that if S ⊆ R is a vector subspace of R, then either S = {0} or S = R.

A: Here, if s={0} then we are done.  But suppose that S⊂ℝ and S≠{0} is a vector subspace of ℝ to prove…

Q: 16. Let V be the set of vectors (x, y, z) E R³ such that r(y?+ z²) = 0. Is V a subspace of R³?

A: Test for subspace for V to be a subspace  If u and v are elements of v then u +av must be in V where…

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

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Q: If S is a subspace of R* and dim(S) = 3, what is the dimension of the orthogonal complement of S?…

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Q: Which of the following subsets S of a vector space V are subspaces? O A. V = R?, S = {(x1,0) : x1 e…

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Q: If W is a subspace of R and v is any vector in R", then ||projwv|+|v-projwv||2= |v||2.

A: Introduction: Every vector that doesn't lie in a subspace can be uniquely expressed as a sum of two…

Q: 12. Let K C R" and let V = { E R" : a1y Vy E K}. Prove that V is a subspace of R".

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: 4 6' Let S be the subspace of R° spanned by the vectors and and let b = 3 Find the point in 4 S that…

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Q: 16. Let V be the set of vectors (x, y, z) E R³ such that r(y²+ z²) = 0. Is V a subspace of R³?

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Q: Prove that if S1 and S2 are orthogonal subspacesof Rn, then their intersection consists of only the…

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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: -4 Find the orthogonal projection ŷ of y onto the subspace 4 W = Span { u1 -5 Uj = u2 Ex: 1.23 : ŷ =…

A: Given

Q: Determine the following is the subspace in R’? W ={(x,y,z):x+y+z=0}

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Q: S= {[a b c]€ R³|a = b+ 1} is a subspace of R. %3D صواب İbi

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Q: Which of the following is a subspace of p2? O a. R2 x, e R W = Зх, + 1 1. Ob. W = ER| x*2 2 0 C. ER?…

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Q: ind the closest point to y in the subspace W spanned by vị and v2 2 y =| 1 |,v1 = ,V2 = |-2 2 а) b)…

A: We will use the following method.

Q: and T are subspaces of V, then SUT

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Q: 16. Let V be the set of vectors (x,y, z) E R³ such that r(y² +z²) = 0. Is V a subspace of R³?

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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: 12. Let K C R" and let V = {x € R" : x ly Vy E K}. Prove that V is a subspace of R".

A: " As per the company guidelines we are supposed to solve first question only. Kindly post the other…

Q: If x is in W, then x is orthogonal to some vector in a subspace W

A: SOLUTION-

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: If W is a subspace of R" and if u is in both W and w then u must be a zero vector.

A: I am going to solve the given problem by using the orthogonal property of a vector.

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,…

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Q: Which of the following are subspaces of R^3?  W ={(x, y, z) :x+y+z=0} W= {(x,y,z): x2 + y2+ z2…

A: The given vector space is R3. We know that a subset W of a vector space V is a subspace of V if it…

Q: Let S = { (a, b, c) ER° : b = a +c}. Show that S is a subspace of R'.

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Q: (A) Let U1, U2, U3 be subspaces of M2x2(R). If V = U1 e U2 e U3, then dim V = 4.

A: So,  V is the direct sum of the subspaces U1, U2, U3  of M2×2(R) , i.e. dim(U1) = dim(U2) = dim(U3)…

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

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Q: 10 - What is the dimension of the subspace below? w = sp {C J. C 9 C 3 a) O 2 b) O 0 1 d) O -1 e) 3.

A: According to question  We have to calculate the dimension of the subspace.

Q: 1. Decide if the following subsets W C V are vector subspaces or not (justify) (a) W = x €RCR?. COs…

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Q: Lct Vị and V2 be subspaces of R" such that Vị C V2. Show that any vector v E R" can be uniquely…

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Q: Let  S=span(e1),  T=span(e2) and  W=span(e1+e3) be subspaces of R3.  S is orthogonal to T, T is…

A: Given that S=spane1 and W=spane1+e3. To prove that S is orthogonal to W. Let x,0,0∈spane1 and…

Q: If V is a 13 dimensional subspace of R20 then the dimension of V- must be

A: Definition of Orthogonal Complements Let V be a subspace of ℝn. Its orthogonal complement is the…

Q: W= ょもt2 Q#5:- Suppose u and W are subspace 4 v. Such that dimU= 5, dimw=6 and dim v = 9. Find dim…

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Q: W = {(x,y,z)eR³:x + z = 0} %3D

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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: Let W be a 3- dimensional subspace of R*, then Dim ( WnW) = Оз O 1 O None of these

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.