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11 Nov 2019
1. Use the Gram-Schmidt process to find the orthonormal vectors qi,42,q3 associated to the vectors a, b,c, the independent columns of A. Then find R and write A as QR. A 0 0 7 0 3 6
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Jean Keeling
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22 May 2019
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3 -1 4. Let A- 4 2 and b 20 10 a) Use the Gram-Schmidt process to find an orthonormal basis for the column space of A. (6 points) b) Factor A into a product QR, where Q has an orthonormal set of column vectors and R is upper triangular. (4 points) c) Solve the least squares solution of Ax b. (6 points)
Let B = {(1, 1, 0), (1, 2, 0), (0, 1.2)} be a basis for R^3. Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal basis for R^3. Use the vectors in the order in which they are given.
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Let B = {(1, 1, 0), (1, 2, 0), (0, 1.2)} be a basis for R^3. Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal basis for R^3. Use the vectors in the order in which they are given.
jadehorse85
Find (u, v) for the inner product (u, v) = 2u_1v_1 +3u_2v_2 +u_3v_3, defined in R^3, where u (5, 0, -5) and v = (8, 6, 13). Find Proj where u = (0, 3, 7) and v = (7, -6, -9). Determine whether the set of vectors {(4, -1, 1), (-1, 0, 4), (-4, -16, -1)} in R^3 is orthogonal (but not orthonormal), orthonormal, or neither. Use the Gram-Schmidt orthonormalization process to transform the basis B = {(0, 4, 8), (8, 0, 0), (1, 1, 1) for R^3 into an orthonormal basis. Use the Euclidean inner product for R^3 and use the vectors in the order in which they are shown.
Show transcribed image text
Find (u, v) for the inner product (u, v) = 2u_1v_1 +3u_2v_2 +u_3v_3, defined in R^3, where u (5, 0, -5) and v = (8, 6, 13). Find Proj where u = (0, 3, 7) and v = (7, -6, -9). Determine whether the set of vectors {(4, -1, 1), (-1, 0, 4), (-4, -16, -1)} in R^3 is orthogonal (but not orthonormal), orthonormal, or neither. Use the Gram-Schmidt orthonormalization process to transform the basis B = {(0, 4, 8), (8, 0, 0), (1, 1, 1) for R^3 into an orthonormal basis. Use the Euclidean inner product for R^3 and use the vectors in the order in which they are shown.
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