There is no linear transformation T\colon \RR^5 \longrightarrow \RR^5 such that the range and kernel of T are the same subspace of \R^5.    True/False ? Explain

Q: Show that a finite union of compact subspaces is compact.

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Q: Consider two subspace of IR": U₁ = span Determine 1 1 2 1 周圍]] -3 a -1 1U2. basis of Uy U₂. U₂-span…

A: Step 1:Step 2:

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = 17 777 || 타타터

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: For each matrix A below, describe the invariant subspaces for the induced linear operator T on F^2…

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

A: Yes , it can be .

Q: Find a minimal spanning set for the subspace spanned by the set of vectors: S={, , , }

A: The given spanning set is S=1, 0, 0, -1, 4, 4, 0, 0. We have to find the minimal spanning set.

Q: Write the equation of a subspace that passes through a point a ∈ R^d and is orthogonal to a given…

A: Let d=3  Now we will find the equation of subspace that passes through a point a€R^3 and orthogonal…

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: Show there is no proper five dimensional subspace of R^5. (i.e. If V is a subspace of R^5 with dim…

A: To Show: If V is a subset of ℝ5, with dimV =5 then V=ℝ5.

Q: Let vl ་ མ། 2 - - ་ -2 and determine if w is in the subspace of R³ generated by v¹ and v². Show your…

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Q: Determine whether the set of vectors is a basis for the subspace of R^n that the vectors span.…

A: The set forms a basis for the subspace of R3 that the vector span.Explanation:

Q: Consider the vectors u1 = (1, 2, 1), u2 = (0, 3, 2) and u3 = (−2, 1, 1). Determine whether the set S…

A: The objective of this question is to determine whether the set of vectors S = {u1, u2, u3} spans the…

Q: 4.33 Does every subspace have a complement?

A: To Check: Every subspace have a complement.

Q: [] : 2x² +8y² ≤1 which represents the set of points on and inside an ellipse in the xy-plane. Find…

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Q: 0 Find the orthogonal projection of 0 onto the subspace of R4 spanned by 121 2 and 20

A: To find the orthogonal projection of the vector onto subspace first check the subspace spanned by…