2.4. Let V be a vector space and let v1, V2,..., Vn be a basis in V. For x = Ek=1 akVk, y = Prove that (x, y) defines an inner product in V. E-1 BiVk define (x, y) := E-1 akBr.

Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

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Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3 )…

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Q: W4 Pick any vector space V that you want, as long as dim(V) ≥ 6. Then, pick 4 vectors in the space,…

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Q: b) Let Pn be a vector space consisting of polynomials of at most degree n. The standard basis for P,…

A: value of k is 0 see calculation below

Q: Suppose {u, } form an orthogonal basis in R2 and y = 2ū - 7 where u = (8) 6 If W = Span{}, what is…

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Q: For the vectors à = (1, 0, −4) and ¯` = (5, 2, 1) what is the scalar a projection of onto a 1/17 √17…

A: The vectors are given by÷

Q: Find an orthonormal basis of the plane x1+ 5x2 – x3 = 0. }

A: Introduction: A set of vectors that is orthogonal to each other and spans a plane is the set of…

Q: 6. Show that the vectors (1,1,0), (1, 0, 1), and (0,1,1) generate F3.

A: In this question, we will show that the given vectors generate F3 .

Q: Apply Gram-Schmidt to (1, 0, −1, 1), (2, 1, −1, 0) , (2, −1, −1, 3) to obtain an orthonormal set…

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Q: Let { u1, U2, Uz, U4, U5} be an orthogonal basis for R5 , y a vector in R5 , W1 Span { u1, Uz} and…

A: Use the direct sum proparty and complement of the subspace for above problem

Q: 2 21 [1] 1 and y = |2 [3. Let u1 = 5 uz and W= Span{u1, U2}. (a) Find an orthogonal basis for W. (b)…

A: Given that, , And, And,…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.