Let R2 have the inner product defined by the positive definite matrix (a) Show that v1 =

Question:

Let R2 have the inner product defined by the positive definite matrix

(a) Show that v1 = (1, 1)T, v2 = (- 2, 1)T form an orthogonal basis.
(b) Write the vector v = (3, 2)T as a linear combination of v1, v2 using the orthogonality formula (5.7).
(c) Verify the formula (5.8) for ||v||.
(d) Find an orthonormal basis u1, u2 for this inner product.
(e) Write v as a linear combination of the orthonormal basis, and verify (5.5).