Find a basis for the following subspace of R°: W3D {(aj + 5а2 — 2а3, 2а1+ 6а2 — аз, Зај + 7а2) : ај, а2, аз € R} -

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

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Q: Determine if the vectors are Linearly Independent or Linearly Dependent. -2 [1 -5 =|2.X2) = -3 ,x6)…

A: A set of n vectors of length n is linearly independent if the matrix with these vectors as columns…

Q: Let v1, v2, v3 be the vectors in R^3 defined by: v1=[0 5 8], v2=[12,-20,5], v3=[-12,15,-13] a). Is…

A: Solution: (a) We see,            v1 + v2 = [0 5 8] + [12 -20 5]                          = [0+12…

Q: y Suppose E (A, B) is controllable. Suppose a change of basis is performed so that we obtain a new…

A: As per the question we are given a controllable system as : ∑ ➞ (A, B) And after a change of…

Q: Determine whether the vectors v₁ = (1, 6, 0, 0), v₂ = (0, -1, 0, 1), v3 = (0, 0, 1, 1), and v₁ = (1,…

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Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

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Q: If possible, find a linear combination of the form w = a₁v₁ + a₂V₂ + a3V3 where v₁ = (2, -1, 4), V₂…

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Q: Determine whether the vectors v₁ = (1, 2), v₂ = (-1,0) and v3 = (0, 1) are linearly independent; if…

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Q: Let Is w a linear combination of the vectors V₁, V₂ and 3? choose 13 -14 -4 --[H], -- [5] -- [13] D…

A: Given that the vectors w=-146 , v1=5-4 ,  v2=-4-3 ,  v3=11 .

Q: Decide whether the vectors [2, 9, -1, 4, 7, 8, 10, 9], [11, 2, 5, -9, 0, 0, -1, 3], [4, 18, -2, 8,…

A: We have to decide whether the given vectors are linearly independent. Then, we can proceed further.

Q: find a vector that is orthogonal to (1,2,3) and (4,5,6). do not use cross product.

A: Let's find vector that is orthogonal to given two vectors.

Q: Find a basis of the subspace of R* consisting of all vectors of the form X1 -8x1 + x2 —6х — 2х2 -6x1…

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Q: Use matrix multiplication to find the orthogonal projection of (-8, 5, 7) on the xy-plane. Let T…

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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: Find a vector that is orthogonal to v. v=

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Q: 17) Let a = [3, -4] and b = [−6, k]. a) Determine the value(s) of k such that a + b = a + 6. What is…

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Q: Let u1 = (4, -2, 1), u2 = (6,3,2) , u3 = (-2,-1,3) find the linear combination v= u1 - 3u2+ 4u3

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Q: Distinguish between a row and a column vector.

A: A column vector is an nx1 matrix because it always has 1 column and some number of rows. A row…

Q: If possible express the vector v as a linear combination of V₁, V₂, and V3. =(0, 0, 0), V₁ = (3, -1,…

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Q: Express the vector -9-7x- 15x² as a linear combination of p₁ = 2 + x + 4x², P₂ = 1- x + 3x² and p3 3…

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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.