:If W is a subspace of a finite-dimensional vector space V, then A. dim(W) = dim(V) always B. dim(W) > dim(V) C. dim(W) < dim(V) D. Data is not complete %3D E. None of the above

Q: -4 Find the orthogonal projection ŷ of y = 4 onto the subspace 3 -3 W = Span { uj U2 = 2 Ex: 1.23

A: With the help of definition of projection of a vector on a subspace, we solve this problem.

Q: 1. If T is a normal operator on a finite dimensional inner product space V and if W is a subspace of…

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Q: If y is in a subspace W, then y - ŷ is not zero. Select one: O True False

A: Solve the following

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

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Q: Consider L = I – A with A : X → X is a compact linear operator in a normed space X. Show that the…

A: The given problem is related with functional analysis. Given that L = I - A , where A : X → X is a…

Q: 3) Suppose TE L(V) and U1, . , Um are subspaces of V invariant under T. Prove that U, ...+ Um is…

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Q: 個同 . Find a basis for the Subspace W of R spanned by S What is the dimension of W?

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Q: 3. If A and B are finite dimensional, orthogonal subspaces of an inner product space V, then show…

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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: If I is a normal operator on a finite dimensional inner product space V and if W is a subspace of V…

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Q: If A is a normed subspace of E, proof that bd(A) is a subspace of X.

A: Please check the answer in the next step

Q: 3. For a certain subspace W, the orthogonal projection of the vector y = |4 onto W 5 is ŷ = | 0 Use…

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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: 10. Let Y = {(x,y,z)| z=-x}. (a) Is Y a subspace of R³? Justify. (b) Is Y a vector space? Justify.

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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: For a certain subspace W, the orthogonal projection of the vector y = 3 onto W is ŷ 2. Use this…

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Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R. %3D

A: To Prove U is a subspace of vector space V 1) 0∈U  If x, y∈U  and a∈V  2) Closed under vector…

Q: If T is a normal operator on a finite dimensional inner product space V and if W is a subspace of V…

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Q: [5 Find the orthogonal projection ŷ of y = onto the subspace 3 W = Span { uį = 2 u2 3 Ex: 1.23 ŷ =

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

A: Two step test

Q: Which of the following choices is not a subspace of vector space R? a. (x,y,z):z=x-y b.…

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Q: 2 Find the orthogonal projection ŷ of y = onto the subspace 3 -2 W = Span { ui u2 Ex: 1.23 ŷ =

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Q: (1) Suppose U and W are both five-dimensional subspaces of R°. Prove that UnW + {0}.

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

A: Orthogonal Subspace

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: Find a basis and dimension of the subspace described as follows:{(x, y, z, w) |2x + 5y – z=0} (0-0)…

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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: If y is in a subspace W, then y - ŷ is not zero. Select one: O True O False

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Q: Suppose V is finite-dimensional, with dim V = n > 1. Prove that there exist 1-dimensional subspaces…

A: Let us consider that (v1, v2, ..., vn) be a basis for V, and let Ui= span(vi), for i ∈ {1, 2, ...,…

Q: 1) Suppose that V is a finite dimensional vector space over R. Prove that every T E L(V) has an…

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Q: II. Decide which of the following are subspaces of corresponding vector spaces: C R?

A: Vector space.

Q: Let W = {(" ):a = 2c = b = –3d} be a subspace of M22. Then dimension of W is equal to: None of the…

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Q: () If S is a subspace in R that is spanned by then S is spanned by: O a. 1 and 0. 1 1 and 1 c. and…

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Q: If W, and W2 are finite - dimensional subspaces of a vector space V, then W + W2 is finite –…

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Q: If V is any three-dimensional subspace of R°, then V has infinitely many bases.

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Q: - Let V = R and W = {(a, b, c) E V \a + b = c}. Is W a subspace of V? If so, what is its dimension?

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Q: Let W = { |xy <0}. Is W a subspace of R?? If so, use generic terms to demonstrate the necessary…

A: W is not a subspace of R2.

Q: = E In > 1} be viewed as a subspace of R. What is the subspace topology on X? A. Discrete B.…

A: Let, y=1n: n≥1 be viewed as a subspace of ℝ.

Q: Let W = {a + bx + cx? + dx*Ia + b = 0 and c – 3d = 0 } be a subspace of P3. Then the dimension of W…

A: Use the concept that dimension of subspace is number of free variables.

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

A: A set B is a basis of a vector space V if its elements are linearly independent and every elements…

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: 4) Suppose u, v E V, where V is an inner product space, and ||u|| = |||| = 1 and (u, v) = 1. Find u…

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Q: If y is not in a subspace W, then y-y is zero. Select one: O True O False

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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: Let V and W be subspaces of R", and dim V and dim W are strictly less than n. Assume that no…

A: To prove: If V and W are subspaces of ℝn such that dim V &lt; n, dim W &lt; n, V is not contained in…

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: (5) Suppose that T E L(V) is such that all subspaces of V of dimension dim(V) – 1 are T-invariant.…

A: Please check step 2 for the solution.!

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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