Find basis for the set of vectors in R2 on the line y= nx . where n=9.

Q: Find an equation of the plane that passes through the point P(2, 5, 1) and has the vector n = (1,4,…

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Q: Find the weighted Euclidean distance between the given vectors. = n with weights w = d(u, v) = Ex: 1

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Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: * Find the values for h for which the vectors are linearly dependent: 7

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Q: a) for which values on are the vectors V3 = 2 %3D 7 19 linearly independent?

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Q: Find the positive t when the vector r(t) = (4t, 4ť, 5t² – 6) is perpendicular to r' (t). -

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Q: find the vector function r(t) given r'(t) and the initial condition

A: Solution: The objective is to find the vector function r(t)

Q: 8. Let C = 2 c=(; 1) - (;) ()- and b = Find a 2-vector z such that Cz = b.

A: we have  C=112-1b=11   we have to find a 2-vector such that  Cz=b

Q: Let L be the line y = 6 – 4x in R?. Find vectors a and b so that v = a+tb is a vector equation for…

A: Vector equation of line

Q: Find a vector function that represents the cur ve of intersection of the paraboloid z a + mnd the…

A: Given that, the paraboloid is z=x2+y2 and the cylinder is x2+y2=22. The projection of the of the…

Q: 3. Find a vector function that represents the curve of intersection of the paraboloid z =. and the…

A: To find the vector function that represents the curve of intersection of the paraboloid z=x2+y2, and…

Q: Find all solutions to r'(t) = v with initial condition r(1) = w, where v and w are constant vectors…

A: Given: r'(t)=v r(1)=w ddtrt = vdrt = v dt Integrate both sides ∫drt = ∫v dtrt = vt + c

Q: 2. Find the magnitude of the vector PQ whose initial point is P(1, 2) and end point is at Q(4, 3).

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Q: Find the next vector spacing and wrap A = 1(x + y?) +jv² + zx) + k(z? + xy)

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Q: 3 (c) Let ¤ = Find the vector in col(A) which is closest to T. 2

A: Consider the matrix  A=[1-1414-21421-10]We first see whether the colums of A are linearly…

Q: Prove that the vector T′(t) is 0 for an object moving in a straight line.

A: Here an object moving in a straight line. The path of the object can be given as follows.…

Q: Find a vector B such that F = V × B and V · B = 0, where F %3D (x + Зу, у — 2z, х - 2z).

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Q: Find the point on the graph of z = 3x2 + y at which vector n = (24, 2, –1) is normal to the tangent…

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Q: Find the spacing and involution for the following vector functions 1- ƒ(x, y, z) = (xi + yj + zk]…

A: Topic:- vector

Q: 3. The work Wdone by = xf + 3xyj - (x + z)k to move a particle from point 1 to point 2 is defined by…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q2] (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A: (A)Consider the given information.Let the ball is defined by the sphere and the equation with radius…

Q: Find the possible values of x if vectors are j +2k, v =2i + j –- k and w = xi+j - k coplanar: u = i…

A: Given vectors are u=i-j+2k, v=2i+j-k and w=xi+j-k. To find the possible values of x if vectors are…

Q: Find the point on the graph of z = 3x2 – 2y? at which vector n = (-12, –16, –2) is normal to the…

A: Shown below

Q: Compute the length of the given vector. (t) = 2t + 7 and q(t) = 7t - 5, where to = 0, t₁ = 1, t₂ = 2

A: We have to find the length of the given vectors.

Q: Find the next vector spacing and wrap A = 1(x +y) +j + zx) + k(2 +xy)

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Q: Find the vectors T and N and the binormal vector B=TXN, for the vector valued function r(t) at the…

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Q: Find a vector function that represents the curve of intersection of the paraboloid z = 2a² + 2y² and…

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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: B) Find a vector parallel to the plane 2x – y – z = 4 and orthogonal to i +j+ k.

A: This is a problem of vector analysis.. we will solve the problem using the concept of vector dot…

Q: Find a set of vectors {u, v} in Rª that spans the solution set of the equations w – x + 2y – 4z 0,…

A: The detailed solution is given below Thank you

Q: The vectors w = x= y = and z = are linearly independent. O linearly dependent. If the vectors are…

A: The solution is follows:

Q: H.W 3- Find a vector V =xi +yj +k that is orthogonal to both A = 3i + j +k _and B = 3i +2j +2k .

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Q: for any R value of the third, so that the following vectors are linearly related and loudspeaker…

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Q: Find a vector function that represents the curve of intersection of the paraboloid z=7x^2+5y^2 and…

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Q: 1. Plot the following vectors using arrows on an xy-graph: -- (}). v-[+]. 1 u = V = 2u, u+v. Is…

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Q: For which value of x do the following vectors form a linearly dependent set in R V =| x, x,

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Q: Find the point on the graph of z = 3x2 + u? at which vector n (24, 2, –1) is normal to the tangent…

A: Gradient of the surface denote the normal direction.

Q: Find a set of vectors {u°, v*} in R4 that spans the solution set of the equations w-x-2y+3z=0…

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Q: For the vector valued function given by 7(t) = (,-1, In t) and u(t) = (t²,-2t, 1) find %3D %3D…

A: Given that r→t=1t, -1, ln t and u→t=t2, -2t, 1 We can write the given vector as r→t=1ti +-1j+ ln tk…

Q: А. Find the domain of the vector position r(t) + t+2 (t + 2) j + In(9 – t²) k

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Q: Consider the two vectors A = Axî + Ayĵ and B = Bxî + Byĵ. If î · î = ĵ • ĵ = 1 and î · j = ĵ · î =…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

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: Find an equation of the plane that passes through the point P(5, 6, 2) and has the vector n = (1,7,…

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Q: Suppose a vector function F(x, y) = 3xi + 2xyj + y ln zk moves along a path C where x = t2, y = t +…

A: The formula to find the work done by the vector function helps to find the required work done. The…

Q: Find the point on the graph of z = 3x2 – 3y? at which vector n = (48, –60, –2) is normal to the…

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Q: Find the vectors T and N and the binormal vector B = T × N for the vector-valued function r(t) = ti…

A: first, we will differentiate the vector r(t) we get  r'(t)=i+2tj+t2k doing the modulus we get…

Q: Evaluate /1+ x² + y²dS, where S is the helicoid with vector equation т(и, 0) - = 0 < u < 3, 0 < v <…

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Q: find the derivitive, r'(t), of the vector function.  r(t)=a+3tb+t^7c

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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.