Compute the coordinates for A₁, A₂ ER where (213 3 with respect to B that is to find λ₁b₁ + λ₂b₂. Compute the coordinates of the standard basis with respect to B.

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A: Theorem 1: Let V be a vector space of dimension n over a field F. Then any linearly independent set…

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A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

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A: Solution:

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A: If set is orthonormal then norm of vector is 1 and scalar product of vectors is 0

A: (.) Given orthogonal basis is,           and  vector (.) Orthogonal basis: A basis  is called an…

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A: Solution to the system

A: Given:u1​=[2−6​],u2​=[124​],x=[2−2​]  Step 1: Check OrthogonalityTwo vectors u1​ and u2​ are…

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A: Note: Observe that the given orthogonal basis spans only two dimension subspace of ℝ4, therefore the…

A: Three vectors form the basis of ℝ3 if and only if the determinant of the matrix formed by the…

A: We find required matrix.

A: We know that two vectors are linearly dependent if one vector can be written as a scalar multiple of…

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