Multivariable and Linear Algebra Homework

Text: Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds by Theodore Shifrin Homework 1: Ex 1.1 : 2,9, 11 Ex 1.2 : 4, 8, 1.3: a, b, c, d, e, f, g,h Ex 3.1: 1 Ex 4: 3,8, 6, 22

Homework 2:

Ex 1.5: 5a, b, 6, 14a, b, Ex 2.2: 1a, c, d, h, k, 7a, 7b Ex 3.3: 3, 4a, b Ex 3.4: 1a, b, c. 2a, b, c, d.

Homework 3:

Rewrite Prop 3.1 proof and Example 3 in own words.

Ex 2.3: 1, 2, 3, 4, 15a. Ex 3.2: 6 (use the same ideas from Prop 3.1).

Pset 4: p.79 1, 2, 3, 4, 5, 9.

(Curves): p .117, 1, 2, 3, 4, 7a, 8b,11

PSet 5 (Linear algebra): p .142, 2, 3a, 4 (must know for real world), 5, 6, 17. p.155, 2a, b. 3a, 3b, 4,

PSet 5 (Linear algebra 2):p.168 4a,5,6,7,8, 14a,b,c, p.221, 2, 3a, b, 4a, 5, 6.

PSet 6（Linear Algebra 3: Least squares, skip to 5.5. Least squares is one of the greatest achievements in applied mathematics, right after the simplex method): 1, 2, 3, 4, 5, 7, 8, 12, 13, 14.

PSet 7 (Intro integration and Linear Agebra 4) p.273, 1, 2, 3, 4., p.421 1,2,3,4, 7

PSet 8 (Eigenvalues): p.433, 1a, b, i, 3, 4, 5, 6, 13. Cool applications: Using diagonalization and 6a, find [1 -1; 1 1] raised to the 2525 power. Finally, to complete the entire freshman first quarter, rewrite example 2 on p.438, which is an eigenvalue proof which is an alternative to Dana's proof.