[Given x₁ = [¹1]¹, ₁ = [¹1¹] ₂ = [100] -me that {Xi), form {x;}. basis vectors. 121,3 reciprocal basic vectors. Express the vector 3 1J⁰ in terms of these basis vectors.

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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Q: Write the vector v = B - 3 8 {[][]}· 8 -2 as a coordinate vector with respect to the basis

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Q: 1) Below, we have a 4 x 4 matrix ,"E", and its inverse. Verify E x inv(E) is a 4 x 4 Identity…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Consider the vectors à = (5,3,7) and b = (2, -3,4). Answer or calculate each of the following.…

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Q: If ū = 2î – î and w = î + 2ĵ, find the compo- nent form of V = ũ + w and sketch the specified vector…

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Q: Find a bif a= (4, - 1,5) ar . b = (-3, 8, 5).

A: Here we will find whether given vectors are orthogonal or not,

Q: What vector v is given by the coordinate vector B = { 9x +4, 4x + 6 }. [3] ? B

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Q: Find the vector X (in standard coordinates) determined by the given coordinate vector [X] and the…

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Q: Consider vectors a = (2, -8), b = (-1, 4), andc = 0. Determine the non-zero scalars a and B such…

A: Consider vectors a=(2,-8) , b=(-1,4) and c=0. We have to determine the non-zero scalars alpha and…

Q: (b) 4x Find any values of x such that the vectors 3 and are parallel X-1 to each other.

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Q: 3. Write ū as a sum of vectors, one in the direction of and another orthoganal to a. 18 [4] -5 [3³]

A: The given vector .The objective is to write the vector as a sum of vectors one in the direction of…

Q: Let A = space of A. Oh=2 Oh=-2 Oh-2 1 3 0 2 -1 Oh 2 2 2-2 Oh can be any real number. . Determine the…

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Q: Show that the vectors are orthogonal.

A: Given vectors are u=<u1, u2>=<4, -1>v=<v1, v2>=<2, 8>

Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: For each of the following sets of compositions, obtain a rational function formula for the…

A: B is the set of compositions of length congruent to 2 (modulo 3).The formula of the Generating…

Q: (a) 3u7 u3 (b) (c) u2 (-2u5) (d) 2u2 : (-u5)

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Q: Write down two unique non-zero vectors à and b in the 5th dimension, R5 (no entry should be 0). a.…

A: The main objective is write two non zero vectors in ℝ5. Find the given values.

Q: Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the…

A: The transpose component is X=1, -3t

Q: Find the unit vector Â, B, the dot product À. B, and state whether these 2 vectors are orthogonal,…

A: Given vectors are- A→=3,-2 and B→=2,4 To find the unit vector A^, B^ and dot product A.B Unit vector…

Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: Are the vectors ū = [4 -5 4], v = [2 2 -3] and w = [-1 -5 2] linearly independent? Choose If they…

A: To find Whether the given vectors are limearly independent or not.