An Elliptical norm for R2 is defined by + 4u2, where x = (1,u). (i) Prove that l is a norm for R2 and sketch the set (x e R2: x, = 1). = 1}.

Q: u= , v=  , w= t is a real number find t so that u,v and w are coplanar

A: Since u, v and w are coplanar, so their scalar triple product is zero, that is  w.[uxv]=0 u x v:…

Q: Find terminal point Q of vector PQ =    <9, −2, 1>   with the initial point at…

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Q: AJKL has coordinates J (2, 4), K (3, 1) and L (3, 3). A translation maps the point J to the point J'…

A: Explanation: Given that, △JKLJ(2,4)→J'(3,3)K(3,1)L(3,3)     Concept Used: To translate the given…

Q: Consider the following vectors. 6, us Apply Gram-Schmidt to find an orthogonal basis for S. (a) S =…

A: a) S=spanu1,u2 orthogonal basis for s=w1,w2w1=u1=4-10w2=u2-u2,w1w1,w1w1     =381-12-8+016+1+04-10…

Q: f) Every continuous map T² RP2 is homotopic to the constant map.

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Q: 2) Write the vector v as a sum of proj span{.…...} (v) and proj spo span{m} orthogonal set V₁,..., V…

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Q: X Edit 10. Rectangle GHU wilth verlices G(2.-1), H7.-1), 17.-4), and

A: Graph plotting

Q: D = 3 u=(9,-4); || u || = -√97 u=(9,-4): || u ||= √97 u=(9,4): ||u||= -√97 u= (9,4); ||u||= √97

A: given u has initial point P at (0,0) and terminal point Q at (9,-4)

Q: Use the function to find the image of v and the preimage of w. T(V₁₁ V₂) = (v₁ + V₂₁ V₁ V₂), v= (5,…

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Q: Find the point on the line T = (-2, 2, 3) + t(4, 1, 1) that presents the shortest distance to the…

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Q: The vertices of AJKL are J(-3, 4), K(3, 0), and L(-5, -4). The equation of the median JLis y = 0.…

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Q: xy² (0) (Use syntax like [3,-4,5] for vectors.) Let F (x, y, z) = xz5 What is the value of curl F at…

A: The vector F(x, y, z) is given. We have to find the value of curl F at (3, 2,1) .

Q: 2s Let H be the set of all vectors of the form Find a vector v in R' such that H span {i}. -s S

A: Spanning set of H

Q: Find ProjS(u) where S is the space spanned by v1= (1/3)(2,1,2) and v2= (1/3)(-2,2,1). Find the…

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

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Q: 123. If F is a vector point function and a is a constant vector then show that i) V (a · F) = (a-V)…

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Q: e vector x²y?

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Q: Show that in 3D space, (a) k EijkEpqk = δip&jq – διαδjp

A: Note:  Since you have posted multiple questions, we will solve first question for you. Kindly repost…

Q: | Let w=z² Find the image of the first quadrant in Z-Plane 2

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Q: Let $K$ is a horizontal shear, next draw a vector $\vec{x}=\left[\begin{array}{l}x_1 \\…

A: Let be the transfomation representing vertical shear of the vector  .Then we have The above can be…

Q: Which among the following diagrams correspond to the metric below on the real plane R^2?…

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Q: (d) Passing through the point (0, 1, 2), perpendicular to the line L and intersects L. L(xo. v) =…

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Q: Find a and b such that v-au bw, nhere u-(1, 2) and w- (1. -1) v - (4, 5)

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Q: 16xydx- 24ydy = -8x²dy %3D

A: The given differential equation can be written as:16xy−24yy' =−8x2y' An ODE Mx, y+Nx, yy'=0 is in…

Q: B Gruien Vectors i = (2,1₁-4), ✓ = (-340,2) w (11213). Find onthogonal projection of u + v along…

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Q: Compute the intersections of the curve xy = 1 and the lines x +y = 5/2, x+y = 2, x+y = 0, x=0 , x=1…

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

Q: Let T be a triangle with vertices (1,-2), (3,0), (-3,2), and f(x,y)=x^2(y-x+3) (a) Find the linear…

A: It is given that T is a triangle with vertices 1,-2, 3,0 and -3,2 and the function fx,y=x2y-x+3. (a)…

Q: Show each vector in the SPAN{sin t, cos t} is a solution of the ODE: y" + y = 0 What are the basis…

A: To find the basis and dimension of the following differential equations