Let W be the subspace of Rª defines as X1 X2 W = {x = ER : : x1 – 3x2 + 4x3 – x4}. %3D x3 X4 Determine dim(W).

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

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Q: Let W = {a + bx + cx² + dx³[ c – 3d = 0 } be a subspace of P3. Then the dimension of W is equal to O…

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Q: The dimension of the subspace W = {A E R™Xn: A is diagonal} is 2. balg j

A: Dimension of the subspace:          If V is spanned by a finite set , then V is said to be finite…

Q: 2. Find the closest point to y in the subspace W spanned by vị and v2. 3 1 -2 y V2 13 3

A: To find  The closest point y in the subspace W spanned by v1 and v2.

Q: For the linear map T = LA : R³ → R³ given by multiplication by A = 300 024 002. find the T-cyclic…

A: Let T be a linear operator on a vector space V and let x be a non zero vector in V. Then the…

Q: Let W = {a + bx + cx² + dx³| a + b = 0,c – a = 0, and d – 3a = 0 } be a subspace of P3. Then the…

A: dimW = 1

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: Let Z E R³ | y Prove that Z is a subspace of R³. = Z

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Q: Let W = {a + bx + cx² + dx°|c - 3d = 0} be a subspace of Pa. Then the dimension of W is equal to 3.…

A: PnF is set of all polynomials of degree nand smaller . PnF denotes the vector space over field F…

Q: Let V = {ax* + bx² + c : a, b, c E R}. Is V a subspace of P4?

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Q: 1. Suppose that A is an nxn non-zero, real matrix and 2 is a fixed real number. Let E ={x=R* : AT =…

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Q: Let W = {a + bx + cx² + dx³[c – 3d = 0 }) be a subspace of P3. Then the dimension of W is equal to O…

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Q: Determine if the set W of vectors (X1 , X2) in R such that x1² + x2 = 0 is a subspace of R?.

A: We have to determine whether W is a subspace of R^2 or not.

Q: Find a basis for the following subspace of IR°. P = {¤ E R° | x1= x3 = x5, x2 + x4 = 0} What is the…

A: Explanation of the answer is as follows

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

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Q: b) Let W = { 0) * x, y e R}. Show that W is not a subspaces of M2x2. %3D

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Q: Consider the subspace of M22 defined by V T(p) by = [PO p(0)] p(0)] = = { [8 a]: a,b € R}, a ER, and…

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Q: at | f = a is a subspace of RI0,1] if and

A: Two step test

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: Suppose V is finite-dimensional and U is a subspace of V such that dim U = dim V. Prove that U = V.…

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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: Determine the dimension of the subspace of R consisting of all XeR* such that x1 + 2x, = 0 and X3 –…

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Q: Suppose V is finite-dimensional and U and W are subspaces of V with W^0 ⊂ U^0. Prove that U ⊂ W.

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Q: Let W = :a +5c = 0} be a subspace of M22. %3D Then dimension of W is equal to: None of the mentioned…

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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: Let W = (a + bx+ cx + dx'|a+ b= 0 and c -3d = 0 ) be a subspace of P Then the dimension of W is…

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Q: Suppose U and W are two-dimensional subspaces of R3. Show that U∩W≠{0}

A: We want to show that  U∩W≠{0}

Q: Let W = {a + bx + cx2 + dx'|c-3d = 0} be a subspace of P, Then the dimension of W is equal to %3D 4.…

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Q: Let W fa + bx + cx2 + dx'| a+ b 0 and c-3d 0 } be a subspace of Pg. %3D %3D %3D Then the dimension…

A: a+b=0  and c-3d=0 b=-a and c=3d Equation given is; a+ bx+ cx2+ dx3  = a- ax+ 3dx2+ dx3 that can be…

Q: If S, is a subspace of R* of dimension 3, then there cannot exist a subspace S, of R* such that Si 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: Suppose that U cr|xyer F4 y EF, U is a subspace of F4- you don't have to! Find a subspace V of F4…

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Q: Prove that the the solution to the equation 2x – y+z= 0 is a subspace of R³.

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Q: Show that the given set V is closed under addition and multiplication by scalars and is therefore a…

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Q: In C[−π, π], find the dimension of the subspace spanned by 1, cos 2x, cos2 x.

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Q: Suppose that X = eR' : 2 + y + z = 0 and r²+y² = z² } . Determine (with justification) whether X is…

A: We have to check whether the set X is a subspace of the vector space ℝ3. We have to give 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 R3 b)show that R' =…

A: Solution of the problem as follows

Q: Let T and T, be linear operators on V and let W be a subspace of V. Show that if W is invariant…

A: Let T1 and T2 be linear operators on V and let W be a subspace of V. If W is invariant under both…

Q: Given two n xn matrices A and B, prove that the set S = {x € R" : ABx = 0} is a subspace of R".

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Q: Let A be an n x n matrix. Verify that V = {x e R" : Ax = 3x} is a subspace of R".

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Q: For a fixed a ϵ R, determine the dimension of the subspace of Pn(R) defined by {f ϵ Pn(R): f(a) =…

A: Assume a ϵ R and the set V=f∈PnR: fa=0 is subspace. Now, assume the arbitrary polynomial f from V.…

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

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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: Is the set M={1/n | n ε z+} compact as a subspace of R?

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Q: For a certain subspace W, the orthogonal projection of the vector y = 5 onto W 4 is ŷ = |1. Use this…

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

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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: Let W = {a + bx + cx2 + dx³| a + b = 0 and c – 3d = 0 } be a subspace of P3. Then the dimension of W…

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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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