2. Consider the vectors W1 = C. W2 W3 [1] a. Explain why these vectors form...
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2. Consider the vectors W1 = C. W2 W3 [1] a. Explain why these vectors form an orthogonal basis for R³. b. Suppose that A = [w₁ W2 w3] and evaluate the product AT A. Why is this product a diagonal matrix and what is the significance of the diagonal entries? Express the vector b = -6 as a linear combination of w₁, w2, and w3. d. Multiply the vectors w₁, W2, W3 by appropriate scalars to find an orthonormal basis u₁, U₂, U3 of R³. e. If Q = [u₁ u₂ u3], find the matrix product QQT and explain the result. 2. Consider the vectors W1 = C. W2 W3 [1] a. Explain why these vectors form an orthogonal basis for R³. b. Suppose that A = [w₁ W2 w3] and evaluate the product AT A. Why is this product a diagonal matrix and what is the significance of the diagonal entries? Express the vector b = -6 as a linear combination of w₁, w2, and w3. d. Multiply the vectors w₁, W2, W3 by appropriate scalars to find an orthonormal basis u₁, U₂, U3 of R³. e. If Q = [u₁ u₂ u3], find the matrix product QQT and explain the result.
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