Exercise 3. Consider R' with its Euclidean inner product. Let U be the plane given by the equation 3r + 2y – z = 0 in R°. a) Find an orthonormal basis b1, b2 for U. b) Find U+ and an orthonormal basis...

Exercise 3. Consider R' with its Euclidean inner product. Let U be the plane given by<br>the equation 3r + 2y – z = 0 in R°.<br>a) Find an orthonormal basis b1, b2 for U.<br>b) Find U+ and an orthonormal basis b, for U+.<br>c) Find the orthonormal projection of v = ( 1) into U.<br>d) Find the orthogonal projection of v = (1) into U+.<br>e) Write the vector v = 1 as a linear combination of b1, b2, bz of R³.<br>

Extracted text: Exercise 3. Consider R' with its Euclidean inner product. Let U be the plane given by the equation 3r + 2y – z = 0 in R°. a) Find an orthonormal basis b1, b2 for U. b) Find U+ and an orthonormal basis b, for U+. c) Find the orthonormal projection of v = ( 1) into U. d) Find the orthogonal projection of v = (1) into U+. e) Write the vector v = 1 as a linear combination of b1, b2, bz of R³.

Jun 05, 2022

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Exercise 3. Consider R' with its Euclidean inner product. Let U be the plane given by the equation 3r + 2y – z = 0 in R°. a) Find an orthonormal basis b1, b2 for U. b) Find U+ and an orthonormal basis...

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