Show that 0 x a =0 = a x 0 for any vector a in V3

Q: Let V be the set of vectors shown below. V= x> 0, y>0 a. If u and v are in V, is u +v in V? Why? b.…

A: Please check step 2 for solution.

Q: If x is an n-vector, show that x + 0 = x.

A: Given, If x is an n-vector.

Q: Show that the vectors (3+ /2,1+V2) and (7, 1 +2\/2) in R² are linear!ly dependent over R but…

A:

Q: Let y= and u= 3 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.

A: Describe y as the sum of vertices x1 in span u and x2 orthogonal to u         x1=α9, 3=9α, 3α and…

Q: Suppose u, v and w are nonzero vectors in 3-space and a is a scalar. Which of the following are…

A: We have to choose the correct answer from the given options

Q: Show that dot multiplication of vectors is positive definite; that is, show that u.u>=0 for every…

A: Show that dot multiplication of vectors is positive definite; that is, show that u.u>=0 for every…

Q: let S= {v, v2,..., v,}a set of vector in vector space V such that CV1+ C2V2+ .. + C, V, = 0 is…

A: Given below the answer

Q: What is the dimension of the vector space S=abc detEM2x3(R): a=b=c=0}

A: Dimension of vector space is number of element in basis

Q: Find a non-zero vector v perpendicular to the vector u = [ -1 ]                          [ 8 ]

A:

Q: Show that there are no vectors u and v such that 11u 11= 1, ||v|| = 2, and uxv= 3.

A: If u and v are two vectors, and the angle between these two vectors is θ Then the magnitude of the…

Q: Show that dot multiplication of vectors is positive definite; that is, show that u . u ≥ 0 for every…

A:

Q: Assume that 0 < a <1 and 0 < b <1.Find the stable vector of 1- a a P = b 1-b w = [ ]

A:

Q: Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

Q: let s={v1, v2... , V, } a set of vector in vector space V such that ... + C, Vn C1V1 + C2 V2 + is…

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Q: A vector u for which || u || = 1 is called a(n)_______ vector.

A: u is a vector whose modulus is 1. u=1 For a vector, if the modulus or magnitude is 1 then the vector…

Q: Let ƒ : R² → R be defined by A if (x, y) # (0,0), f(r, y) = if (r, y) = (0,0). Determine the nonzero…

A: According to the given information, it is required to determine a non-zero vector u = (h,k) for…

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector - [';" - a 1 - ] a P = b

A: From the given information, P=1-aab1-b Let, stable vector as, w=xy

Q: Let nonzero vectors ū,v,weR be linearly independent. Show that there does not exist a nonzero vector…

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Q: ): Let v = 3 be two vectors in R. and v2 %3D Show that v = belongs to span{v1, v2}. 62

A: We know that if vector "v" is linear combination of "v1" and "v2" then vector "v"belongs to the span…

Q: show that the given vector functions are linearly independent on (−∞,∞).

A: To show that the given vector functions are linearly independent x1t=   et-et,        x2t=etet

Q: 4. Prove that, for any vectors A, B and C, that a necessary and sufficient condition А x (Вx С) %3…

A: The solution is:

Q: Write the vector x=0 as a linear combination of the vectors u=0, v= 1, w= 1 1

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Q: Show that for any vector u in R^n, (u^(T))*(u) = 0 if and only if u = 0.

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Q: Prove that if vector u is orthogonal to both vectors v and w, then u is orthogonal to v + w.

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Q: Show that there are no vectors u and v such that llull = 1, llvll = 2,and u·v= 3.

A:

Q: Let u = u1i + u2j + u3k, v = v1i + v2j + v3k, and w = w1i + w2j + w3k be vectors in R3. Show that

A: given: u=u1i+u2j+u3kv=v1i+v2j+v3kw=w1i+w2j+w3k we have to show that: u×v.w=u1u2u3v1v2v3w1w2w3

Q: Give an example of a linear combination that resulted in the zero vector that did NOT have 0's for…

A: Query- Give an example of a linear combination that resulted in the zero vector that did NOT have…

Q: Show that if u is a vector in R2 or R3, then u + (−1)u = 0.

A: The objective is to show that if u is a vector in R2 or R3 then u + (−1)u = 0. Suppose u and O is a…

Q: Let y = 18 || = and u = 6 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and ₂…

A: Given that                   y→=-4-3 and u→=66.

Q: Find the norm of x and the unit vector ü in the direction of x if ||| = u =

A:

Q: Prove that a·a= = |a|2, where a is a vector with n components

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Q: If v is a vector in R", and if k is any scalar, then: (a) ||v|| 20 (h) x = 0 if and only if y = 0

A: Given: v is a vector in ℝn and k is any scalar To show that  a) v≥0 b) v=0 if and only if v=0

Q: Find the weighted Euclidean norm of the given vector. 10 with weights w = v = ||v|| = Ex: 1

A: Here, we need to find the weighted Euclidean norm of the vector v=102 with the weights w=111. Let…

Q: prove that 12 div A; = √√√x² {√8 8¹k Ax} = dxr div A¹, where A; and Ai are the covariant and…

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Q: 2. Let i= and (a) Compute the length of the vector u.

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Q: Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify

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Q: Show that if u is a vector in R2 or R3, then u + 0 = u.

A: To show that if u is a vector in R2 or R3, then u + 0 = u.

Q: Let y = and u = 3 Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal…

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Q: Let u= 2 and v= 2. Show that among all the scalar multiples cv of the vector v, the projection of u…

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Q: Find the best approximation to z by vectors of the form cv1 + ¢2V2. 3 1 -7 -1 1 V1 V2 -3 3

A: To find  The best approximation to z by vectors of the form c1v1+c2v2.

Q: Express the vector 2x2 + x + 3 in the space P2 as a linear combination of the vectors p = -x2 + 1, q…

A:

Q: ind the norm of x and the unit vector u in the direction of a if -5 * = ||| = %3D 2 2

A: The norm of a vector A→=abc is defined by A→=a2+b2+c2.

Q: Let u and v = .A vector orthogonal to both ú and v is

A:

Q: The vector 1 is in Span{ V2, ., Vm } if and only if ( V1..., Vm ) are linearly dependent. O True…

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Q: Write y as the sum of two orthogonal vectors, x1 in Span{u} and x2 orthogonal to u

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Q: Find a vector x whose image under T,

A: A=12541022011-4-9-21 ,b=12543-51The augmented matrix of the system is 12541022011-4-9-2112543-51now…

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.