1] Suppose that W, N are non-zero two- dimensional vectors which are not parallel. Show that if C is any two-dimensional vector then it can be written as a linear combination of the given vectors: that is show there exist s, t e R such that C = sW + tÑ.

Q: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: If i = (a, b, 0), ï = (a, 1, 6), and (1,1, 12) are vectors in R Determine the value of b so that and…

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Q: u = (2, 3,-1) v= (0, 1, -2) w = (2, 4, -3).

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Q: Why are there no vectors u and v in R,, such that ||u.||= 2, ||v|| = 3, and    uxv= -7?

A: The given values are, u=2, v=3,   and  u×v=-7. The objective is to find the valid reason for the…

Q: 7. "Let &, n, ở be real numbers and consider vectors (1,5,8²); (1,n,n²); (1,0,0²). Determine the…

A:

Q: v, =,v, =, v, =

A: To add or subtract two vectors, add or subtract the corresponding components of each vector. For…

Q: A sum of scalar multiples of two or more vectors (such as c,u + c,v + c,w, where c, are scalars) is…

A:

Q: If a vector space V contains 4 linearly independent vectors, then dim(V) > 4. true false

A: Given ,  If a vector space V contains 4 linearly independent vectors , then  We have to check dim(V)…

Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

A: Solution

Q: If vector a= and vector b= are vectors a and b orthogonal, parallel, or neither? Provide

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Q: Prove that the set of vectors B = {(1,2,3), (3,2,1),(0,0,1)} is linearly independent and spans R³.

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Q: 11. If ā.b = 0, why can we not necessarily conclude that the given vectors are perpendicular? (In…

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Q: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

A: Given: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

Q: For what values of m and n are vectors [m,n,1], [2,1,3] and [2,1,1] coplanar?

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Q: Two linearly independent vectors in R3 span R2, is that true

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Q: If a plane is parallel to one of the coordinate planes, then its normal vector is parallel to one of…

A: We will solve the problem

Q: Find a nonzero vector orthogonal to the plane through the points P, Q and R if P(1,0,0), Q(7,8,0)…

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Q: Consider the vectors in R2 3 2 (3) Express as a linear combination of the vectors Select one:…

A: Here we have to find the linear combination.

Q: 1. Show that the following vectors are linearly dependent. Uz = U3= %3D -2 3.

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Q: 8.) find a vector of norm 2 that is orthogonal to the three vectors, u=(2,1,0), v=(-1,- 1,0) and…

A: Just assume a vector and apply criteria of perpendicular of two vectors ..as I have done solution in…

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

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Q: linear algebra question:

A: The orthogonal projection is given by,

Q: 2. Let y and u = Write y as a sum of two orthogonal vectors, one in Span{u} and a vector orthogonal…

A: y and u are given to us and we need to write y as a sum of two orthogonal vectors such that one is…

Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: #7. Given that the three 3-dimensional vectors v1 = (- 1,3, - 4), v2 = (3, – 8, 10), v3 = (2, – 9,7)…

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Q: . Suppose ū = and i = ;). Construct a pair of orthogonal vectors from these two vectors.

A: See below the answer

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, -4,0), v = (-1,-1,2,2), and…

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Q: -2 Show whether or not the vector bs is a linear combination of the vectors a, = az = and az = that…

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Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…

Q: 2. Suppose that u, v and w are vectors in 3-space such that ||u|| = 5, u·v = 7, and u · w = -3 а.…

A: Answer

Q: 19. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, –4,0), v = (-1,–1,2,2),…

A: Step:- 1 Given that u=2, 1, -4, 0,  v=-1, -1, 2, 2,  w=3, 2, 5, 4 Now, first we check the given…

Q: Find two vectors in opposite directions that are orthogonal to the vector        u = ⟨3, 1, −2⟩

A: u=3, 1, -2 Let v=a, b, c be the vector orthogonal to the vector u=3, 1, -2. Then, u·v=0…

Q: Find a nonzero vector orthogonal to the plane through P(2,5, 1), Q(-3, 1, –2) and R(5, –3, –1).

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Q: Find a unit vector that is orthogonal to both u = (2, -8, 6) and v = (4, 10, -6).

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Q: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=<2,-2,1>.

Q: Let x = (1,2,3) and y = (1,1,1) Project y on x (in econometrics, this may be denoted by Px). Are the…

A: We will first write the formula for projection of a vector onto another vector b .

Q: Answer the following questions: 1] Suppose that W, N are non-zero two- dimensional vectors which are…

A: Concept:

Q: Show that if C is any two-dimensional vector then it can be written as a linear combination of the…

A: Given: C→ be any two dimensional vector spaceie.,   C→=x,y|x,y∈ℝFormula: Convex set∃ t,s∈ℝ such that…

Q: (2) Given the vectors - -- -- --- 1 V1 = V2 = V3 = and w = are there scalars a, b, and c such that…

A:

Q: 1] Suppose that W, N are non-zero two- dimensional vectors which are not parallel. Show that if C is…

A: We have to solve given problem:

Q: Let y→=[−8, −7] and u→=[−2, 6]. Write y→ as the sum of two orthogonal vectors, x→1 in Span{u} and…

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Q: Find a nonzero vector orthogonal to the plane through P(2, 5, 1), Q(-3, 1, – 2) and R(5, –3, –1).

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Q: 3. Show that that the vector u = |-5 is a linear combination of the vectors vị = |-3 3 2 V2 = -4 and…

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Q: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³

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Q: Let

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Q: Prove that two vectors are linearly dependent (taken as a set of vectors) if and only if one vector…

A: Let X and Y be two vectors. Suppose these two vectors are linearly dependent. [To prove: One vector…

Q: Suppose that two vectors T and ỹ in R" are orthogonal, meaning their inner product satisfies ·g = 0.…

A: This is a problem of vector calculus.

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.