What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 = (14, 2, 8)

Q: Find one voctor in R' that spans the intersoction of U and W where U is the xy-plane-that is, U =…

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Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

Q: Find a vector of norm 1 that is orthogonal to the three vectors ü = (2,1,-4,0), v=(-1,-1,2,2),…

A: We have to find a vector of norm 1 which is orthogonal with the vectors u, v and w. Let a, b, c, d…

Q: Determine a vector that is orthogonal to both (1, 2, -1) and (3, 1, 0).

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Q: What is the size of the space stretched by the vectors {(1,0,2),(2,1,4),(1,-1,1)}?

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Q: Find 3-dimensional vectors V₁, V₂, V, satisfying V₁V₁ = 4, ₁₂ = -2, V₁ V₂ = 6, V₂ V₂ = 2₁ V₂ V₂ =…

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Q: A vector orthogonal to the plane through the points (-1,0, 0), (0, 0,-2), (2, 3, 4) is

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

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, -2, -2), (2, 3, 4) is < 2, – 10, 6…

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

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

Q: Express the vector (-1, 0) as a linear combination of the vectors (-1, - 1) and (-1, 1). (-1,0) =…

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Q: Express the vector u = (1,-8,0) as linear combination of the vectors u, =(4,5,0) and u, = (7,6,0)…

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Q: Fnd a basis of the Subspaca of R* by five vectors spanned (1,2,1,-1) (10,15,15, 0 (3,4,5,1)…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: The two vectors u=(-2,3,1,4) and v= (1,2,0, -1) are orthogonal in the vector space R4 True False

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Q: Are the vector spaces R4, M2,2, and M1,4 exactly the same? Describe their similarities and…

A: We have to determine if the vector spaces, are exactly the same or there is any similarity or…

Q: Consider the vectors [2, 1,0,0], [3, 1,0,0], [0,0,0, 1] in R'. Find a vector v so that v, [2, 1,0,…

A: We know four vectors v1 , v2 , v3 and v4 in ℝ4  will be linearly independent iff , av1→ + bv2→ +…

Q: Find two unit vectors orthogonal to both u = (1, 2, – 3) and = (0, 1, 2). %3D unit vectors =

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Q: Find projection of vector (0, 1, 0) into the line spanned by (0, 1,0) 0(-1,0, 2) 0(-1,3, 2) O (0, 3,…

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Q: In a 4-D Euclidean plane, vectoru = (a, b, c, d). In a 3-D space, vector v = (2,7,c). What is u + v?…

A: Given :  Vector u = &lt;a, b, c, d&gt;  Vector v = &lt;2, 7, c&gt;     To find the vector u + v.

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, –2), (2, 3, 4) is

A: Query- Find a vector orthogonal to the plane through the points -1,0,0,0,-2,-2,2,3,4. Answer- Let…

Q: Find two vectors of norm 1, orthogonal to all the vectors u = (2, 1, 4, 0), v = (−1, −1, −2, 2), w…

A: Given data:- u=2,1,4,0v=-1,-1,-2,2w=3,2,5,4

Q: Find projection of vector (0,1,0) into the line spanned by (0,1,0)

A: We have to find the projection of the vector (0,1,0) into the line spanned by (0,1,0).

Q: Consider the vectors (2, 1,0, 0), [3, 1,0, 0], [0,0, 0, 1] in R". Find a vector v so that v,…

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Q: how can one check that a set with two operations, addition and scalar multiplication, is a vector…

A: One can check for a set to be a vector space by checking all the above axioms. If a set V with two…

Q: fx and y are two n-vectors, then prove that 1 1 -+-=1 (Holder inequality) (b) xy, <,, (Schwarz…

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Q: Find a vector orthogonal to both (-3, 2,0) and to (0, 2, 1) of the form (1,

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, -2), (2,3, 4) is

A: A vector orthogonal to the plane through the points (-1,0,0) , (0,-2,-2) , (2,3,4) is

Q: Show that the point 1, - 2, 0 lies on both planes 3x-2y+z=7 and x-4y-2z=9. Hence, find the vector…

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Q: The vectors [1, 0, 1], [1, 1, 1] and [1, 0, -1] are coplanar. True False

A: Using coplanarity conditions we have

Q: Find a Vector ū: non zero Vector perpendicular to the

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Q: Determine the vector projection of the vector (5,0, 7) on the vector (–1,3,4).

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Q: The terminal point of the vector v = i +2j +3k with initial point (4, 2, –3) is

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Q: Find the scalar and vector projections of b onto a. а - (-4, -3), ь - (6, 0) compab projąb

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Q: (2, -3 ,1),(2, -3 ,5) Express the space stretched by the vectors with cartesian equations.

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Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

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Q: 8. Show that the cross product u x v of the vectors u = (-3, 5, -4) and v = (-3, -5, -5) is…

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0,0, –2), (2,3, 4) is О О O 6,-10, 3>…

A: Let, Given vectors are P(-1,0,0), Q(0,0,-2) and R(2,3,4). We have to find non zero vector orthogonal…

Q: find vector v that is orthogonal to vector (0,1,0,0,0) Select one: a. v=( r, 0, s, -t, w) b. v=( r,…

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Q: 2. Which does not exist for a line in three-space? a) vector b) parametric c) symmetric d) scalar

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Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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Q: Find a vector u € R' such that, at the point (2, 1, -1), the function f(, v, 2) =-y + 2a2 + has its…

A: Given, f(x,y,z)=-y3+2x2+z2

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 0, -2), (2, 3, 4) is

A: We will solve the problem

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: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is

A: This could be solve using vector concept.

Q: Find the length of the vector. v = (5, 0, 3, -2) %3D ||v|| = %3D

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1, -2), (2, 3, 4) is

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Q: determine projection of the vector b = -1 1 1 on the space generated by the vectors {--E)--[ -[+]}…

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Q: Find a vector of norm 1 that is orthogonal to the three vectors u = (2,1,-4,0), =(-1,-1,2,2),…

A: The solution is given as

Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: Verify the Cauchy-Schwarz Inequality for the vectors. a = (1, 1, -2), b = (1, -3, -2)

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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.