Find an orthogonal basis for the vector space spanned by 0 and 2

Q: Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1,…

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Q: state a vector with all non-zero entries which is orthogonal to v⃗

A: Given v vector  Let w vector be orthogonal to v vector  Then w vector . v vector = 0

Q: Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is…

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Q: The vectors --[+]»-[i]»-[3]m² -]»-[3]»=[] V2 = span R2 but do not form a basis. Find two different…

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Q: -9 -10 12 -15 A = 4 -8 6. Find a non-zero vector in the column space of A. 69

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Q: Show linear dependence in part (ii) to show that ({1,0,1}) is a basis.

A: From part ii)We have to show that the set  is a basis of .We know thatA basis B of a vector space V…

Q: Find a basis of R3 that contains the vectors (1,0,1) and (1,-1,1)

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Q: Determine whether the set of vectors {(2,-1,3),(4,1,2),(8,-1,8)} form a basis for R3.

A: Consider the vectors : 2,-1,3, 4,1,2, 8,-1,8 To form a basis these vectors, the vectors must be…

Q: -9 -10 12 -15 A = 4 -8 6 6 0 9

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Q: 4. Find representation of the vector v = 2 – 2x+ 6x? with respect to following basis. {1+ 3x + 3x?;…

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Q: Please discuss your understanding of what a basis is for a vector space

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Q: Prove that a(-3,2) and b (2,-3) form basis vectors in xy plane

A: a set is said to be basis if set is linearly independent and it spans the space.

Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

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Q: d). Let K = {(x;y) | x,y e R} with operations (x1;y1) (X2;y2) = (x, + x2 + 1; y, +y2 - 2) %3! (ax, +…

A: Given: K=x;y | x, y∈ℝ with operations x1, y1⊕x2, y2=x1+x2+1; y1+y2-2 and a⊗x1;y1=ax1+a-1; ay1-2a+2.…

Q: Let v1=( 0 1 -1 2)^T v2=(1 0 -2 1)^T Let V=Span{v1,v2} Find a basis for the orthogonal complement of…

A: Orthogonal complement : Let V be a vector space in ℝn. The orthogonal complement is the subspace…

Q: Find a subset of vectors v1 = (1,0,1,1), v2 = (-3,3,7,1), v3 = (-1,3,9,3) and v4 = (-5,3,5, –1) that…

A: To find subset of vectors that forms a basis for the space spanned by the vectors. Form a matrix:…

Q: 3) Find a basis of F3 containing the vectors (1, 2, -3), (2, 6, -3)

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Q: Identify all the polynomial functions of two variables of degree < 2 which are harmonic. Show that…

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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.