Prove that the set of n vectors constructed in the proof of Theorem 1.5 is linearly independent. (Hints: We started with a linearly independent set {w1, . . . ,wnd }. Suppose akvk + ciwi + dsus = 0. Multiply by A I and check that we get only a linear combination of the wi , which are known to form a linearly independent set. Conclude that all the ds and ci , i _= 1, j1 + 1, . . . , j1 + 1, must be 0. This leaves only the terms involving the eigenvectors w1, . . . ,wj1+1, and v+1, . . . , vd , but by construction these form a linearly independent set.)

L8 - 10 Now You Try It (NYTI): 1. Evaluate the limits, if possible. 1 − 1 x x − 12 (a) lim x→4 x − 4 √ √ x +2 − 2 (b) x→0 x 4 − x (c) li+ x→3 ln(x − 3)...