3.6 # 2. Prove that there is a unique real number x such that for every real
number y, xy + x 4 = 4y.
Review for Linear Algebra Final
Application: Voting theory
I have decided that this topic will not be covered on the nal exam.
6.1 Inner products
Vocabulary: inner product, inner product space, weighted Euclidean inner product, norm/
length, distance, u
Formula Sheet for Linear Algebra Final
6.3 Orthonormal bases; Gram-Schmidt process; QR-decomposition
Apply the Gram-Schmidt process to a set cfw_v1 , v2 , . . . , vr of vectors to obtain an orthonormal set cfw_q1 , q2 , . . . , qr of vectors with the s
Review for Linear Algebra Midterm 1
1.1 Introduction to systems of linear equations
Vocabulary: linear equation, system of equations, solution set/general solution, (in)consistent
system, augmented matrix.
Determine whether an equation is linear.
Give an example (not a proof) of the objects introduced in the
problems with an .
4.5 2,6,16,19 4.6 2, 4, 10b, 13, 17, 18, 20,
Ifweassumexandy are arbitrary elements of A, xRy, and
b a b,alsoa Ourgoalof|a|
Given a b, if we assume a 0 then we can conclude a b. Therefore, for all real
numbers a and b, |a| b iff b a b.
(b) Prove that for any real number x, |x| x |x|.Given that for a