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- Use the inner product u,v=2u1v1+u2v2 in R2 and Gram-Schmidt orthonormalization process to transform {(2,1),(2,10)} into an orthonormal basis.What will happen if the Gram–Schmidt process is applied to a set of vectors {v1, v2, v3}, where v1 and v2 are linearly independent, but v3 ∈ Span(v1, v2). Will the process fail? If so, how? Explain.What will happen if the Gram–Schmidt process is applied to a set of linearly dependent vectors {v1, v2, v3} such that v1 and v2 are linearly independent, but v3 ∈ Span(v1, v2)? Will the process fail? If so, how? Explain.
- Apply the Gram-Schmidt process to transform the basis vectors V1= (1,1,1), V2 = (0,1,1), V3 = (0,0,1) into an orthogonal basis (u1,u2,u3) and then normalize the orthogonal basis vectors to obtain an orthonormal basis (w1,w2,w3)Find an orthonormal basis spanned by a set of vectorsV1 = (2, 2, 1), V2 = (−2, 1, 2), V3 = (9, 0, 0). (Use Gram-Schmidt Process).use the Gram–Schmidt process to generate an orthogonal set from the given linearly independent vectors.
- Find the orthonormal set of vectors from A = { [1, 1, 1], [1, 1, 0], [1, 0, 0] } using the Gram-Schmidt process.Is the set of vectors an orthonormal basis? Otherwise, use the Gram Schmidt process to find the orthonormal basis for R³!Use Gram–Schmidt orthogonalisation to construct a set of three orthonormal vectors in a space of dimension N = 3 by starting from b1, then using b2 and b3 in that order.
- Let's try to the Gram-Schmidt process of orthogonalization with the matrix 0.223 0.668 0.710-0.125 0.741 0.660 0.795 -0.234 0.560 What is the x-coordinate of r2-prime? (don't normalize r2-prime, simply follow the steps) Round your answer to 3 decimal places.Calculate the first two vectors generated by the Jacobi method.Good morning, could you help me with that? Thank you very muchEstablish a vector basis for the set of matrices of dimension mxn and say what is its dimension.of what dimension is that vector space?