Psych 150
Temperament
TopHat
Temperament
If personality traits have genetic foundations they
should
be visible in early childhood
show some kind of temporal stability across the lifespan
Temperament
Inherited personality traits present in early child
Summer 2015
MATH 129A, Linear Algebra I
HOMEWORK
What we learn to do, we learn by doing. Aristotle (384-322 BC)
Homework 1, due June 4 (Th) in class
Ex1.1 # 13, 18, 21, 25, 30
Ex1.2 # 1, 4, 13, 16, 30
Ex1.3 # 5, 10, 13, 18, 25
Ex1.4 # 3, 15, 22, 30, 3
Summer 2015
Answers of section 6.5
6.5 # 1
(a) normal equation:
6 11
11 22
x=
4
11
3
2
(b) x =
5t
6.5 # 6 x = 1 + t where t R
t
6.5 # 10
4
(a) 1
4
(b) x =
3
1/2
7
3
6.5 # 14 Au = 8 , and so Au b = 24. On the other hand, Av = 2 , and so
8
2
22 20
Au b = 2
Computer Project: Visualizing Linear Transformations of the Plane
Name_
Purpose: To understand the standard matrix of a linear transformation. In particular, to see the geometric effect of how a
2x2 matrix transforms R2 ; and conversely, to learn how to w
Computer Project: Roundoff Error in Matrix Calculations
Name_
Purpose: To see some of the effects of roundoff error by solving a variety of linear systems, using three different
algorithms. Some of these problems involve poorly conditioned matrices.
Prere
Computer Project: QR Factorization
Name _
Purpose: To learn to use MATLAB's qr function and understand the connections between the matrices it produces
and the QR factorization described in the text.
Prerequisite: Section 6.4
MATLAB functions used: qr; an
Computer Project: Using Eigenvalues to Study Spotted Owls
Name_
ATTACH YOUR PLOTS AND TURN IN WITH THIS PAPER.
Purpose: to use eigenvalues and eigenvectors to understand the dynamics of this population and determine
experimentally the critical rate for su
Computer Project: Getting Started with MATLAB
Name_
Purpose: To learn to create matrices and use various MATLAB commands. Examples here can be useful for reference
later.
MATLAB functions:
[] : ; + - * ^
size, help, format, eye, zeros, ones, diag, rand, r
Summer 2015
Answers of Homework 2
1.7 #2 linearly independent b/c the RREF has pivot in every column
1.7 #7 linearly dependent b/c the RREF does not have pivot in every column
1.7 #10
a. No h will work.
b. Any h will work.
1.7 #27 4 because the matrix mus
Summer 2015
Answers of Homework 1
1.1 #13
The solution is (5, 3, 1).
1.1 #18
Yes, because the last column of RREF is not a pivot column.
1.1 #21
h can be any real number.
1.1 #25
The system is consistent if and only if k + 2g + h = 0.
1.1 #30
1
R2
5
R2 ,
Psych 150
Heritability:
Nature vs. Nurture
TopHat
Determining the Role of Inheritance
Behavioral genetics
genetic influences on behavior, cognition, and emotion.
tease apart genetic vs. environmental influences
Twin studies
Compares identical and fra
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Summer 2015
MATH129A Linear Algebra I
TEST 1 Solution
Please report any typos and errors. If you dont understand, ask for clarication.
1. (a) False
(b) False
(c) True
(d) False
(e) False
2. (a) R3
(b) (2)R2 + R1 R1
(c) Those matrices in REF are:
2 3 0
0
Summer 2015
MATH129A Linear Algebra I
Sample Questions
1.
[10] True or False questions, explanation is NOT needed. Correct answer worths 2
points, incorrect or no answer worths 0 point.
(a)
If x is orthogonal to both u and v, then x must be orthogonal to
Summer 2015
MATH129A Linear Algebra I
Sample Answers
1.
(a) True
(b) True
(c) False
(d) False
(e) False
2.
(a) Circle 2nd and 3rd matrices in the rst row, and 3rd matrix in the second row.
(b) a basis is
1
4
1
0
0
,
0
3
0
1
1
3.
(a) Yes, the
Summer 2015
MATH129A Linear Algebra I
TEST 2 Solution
Please report any typos and errors. If you dont understand, ask for clarication.
1. (a) False
(b) True
(c) True
(d) False
(e) True
2. (a) XY =
a
2
0
1
0 ab 3a
0 2b 6
0 0
0
0 b 3
(b) h = 3
(c) there ca
Computer Project: Least Squares Solutions and Curve Fitting
Name_
Purpose: To practice using the theory of Least Squares by calculating and plotting the Least Squares line, quadratic curve,
and cubic curve, and the error for each, for two sets of experime
Computer Project: QR Method for Calculating Eigenvalues
Name _
Purpose: To see how eigenvalues can be calculated by iterative methods that employ QR factorization, and get some
understanding of why such methods work. This type of algorithm is used in all
Computer Project: Real and Complex Eigenvalues
Name_
Purpose: To see examples of nonreal eigenvalues, and to learn how to use MATLAB's eig function.
Prerequisites: Sections 5.1 and 5.5.
MATLAB functions used: eig, *, and cxeigdat from Lay's Toolbox
1. (ha
Computer Project: An Economy With an Open Sector
Name _
Purpose: To study a linear system model of an open sector economy.
Prerequisites: Sections 2.1, 2.7
MATLAB functions used: - ,rref, sum, eye; and Lay's Toolbox
Background. This is based on Exercise 1
Computer Project: The Adjacency Matrix of a Graph
Name_
Purpose: To learn about graph and adjacency matrix, to see how the powers of the adjacency matrix provide
information about the graph and vice versa, and to apply these ideas.
Prerequisite: Section 2
Computer Project: Counting Floating Point Operations in Matrix Products Name_
Purpose: To count the number of arithmetic operations done in certain matrix products and see that the placing of
parentheses can make a difference in some products.
Prerequisit
Computer Project: Exchange Economy and Homogeneous Systems
Name_
Purpose: Solve a homogeneous system to find equilibrium prices for an exchange model economy.
Prerequisite: Section 1.5
MATLAB functions used: -, /, eye, sum; and econdat and rref from Lay's
Computer Project: Rank and Linear Independence
Name_
Purpose: To define rank and learn its connection with linear independence.
Prerequisite: Section 1.6
MATLAB functions used: ' , rank; and indat, rref and randint from Lay's Toolbox
Definition. The rank
Computer Project: Practice Row Operations
Name _
Purpose: To practice calculating the reduced echelon form with individual row operations
Prerequisite: Section 1.2.
MATLAB functions used: - , / ; and replace, swap, and scale from Lay's Toolbox
Background:
Computer Project: Elementary Analysis of the Spotted Owl Population
Name _
ATTACH YOUR PLOTS AND TURN IN WITH THIS PAPER.
Purpose: To study the owl population with several different survival rates for juveniles.
Prerequisites: Section 1.9 and the example