Sample Final Exam
... Thus, 3a + b = 0, so b = −3a. Thus, we can write p(x) as p(x) = ax2 − 3ax + c = a(x2 − 3x) + c Thus, every polynomial in S is in the span of the polynomials x2 − 3x and 1. Since these polynomials are linearly independent, they form a basis for S. Thus, a basis for S is {x2 − 3x, 1}. 4. Suppose that ...
... Thus, 3a + b = 0, so b = −3a. Thus, we can write p(x) as p(x) = ax2 − 3ax + c = a(x2 − 3x) + c Thus, every polynomial in S is in the span of the polynomials x2 − 3x and 1. Since these polynomials are linearly independent, they form a basis for S. Thus, a basis for S is {x2 − 3x, 1}. 4. Suppose that ...
Octave Tutorial 2
... • build vectors and matrices using different notations and appropriate built-in functions; • construct new vectors and matrices from existing ones; • extract and change single elements or subsets of vectors and matrices. Octave is a program specially designed for manipulating matrices. Simply speaki ...
... • build vectors and matrices using different notations and appropriate built-in functions; • construct new vectors and matrices from existing ones; • extract and change single elements or subsets of vectors and matrices. Octave is a program specially designed for manipulating matrices. Simply speaki ...
Introduction to MATLAB Part 1
... Number Display • Scientific Notation – Although you can enter any number in decimal notation, it isn’t always the best way to represent very large or very small numbers – In MATLAB, values in scientific notation are designated with an e between the decimal number and exponent. (Your calculator prob ...
... Number Display • Scientific Notation – Although you can enter any number in decimal notation, it isn’t always the best way to represent very large or very small numbers – In MATLAB, values in scientific notation are designated with an e between the decimal number and exponent. (Your calculator prob ...
lab chapter 5: simultaneous equations
... Norms can be used to determine how similar two vectors are. It was easy to see that equations (5.2) were singular because they are a small system. That determination would be more difficult if we were dealing with, say, 100 equations and 100 unknowns. Norms provide us with an efficient mathematical ...
... Norms can be used to determine how similar two vectors are. It was easy to see that equations (5.2) were singular because they are a small system. That determination would be more difficult if we were dealing with, say, 100 equations and 100 unknowns. Norms provide us with an efficient mathematical ...
1 DELFT UNIVERSITY OF TECHNOLOGY Faculty of Electrical
... a scalar, equal to the length of the first vector times the length of the projection of the second vector on the first vector. a vector with length equal to the area of the parallelogram spanned by the two vectors. a vector with length equal to the length of the first vector times the length of the ...
... a scalar, equal to the length of the first vector times the length of the projection of the second vector on the first vector. a vector with length equal to the area of the parallelogram spanned by the two vectors. a vector with length equal to the length of the first vector times the length of the ...
Homework assignment on Rep Theory of Finite Groups
... (1) If a group G acts on a set S and s is in S, then the stablizer of s is Gs = {g ∈ G|gs = s}. The orbit of s is the set Os = {gs|g ∈ G}. (a) Prove that Gs is a subgroup of G. (b) Find a bijection between cosets of G/Gs and elements of Os . (c) Show that |Os | = |G| / |Gs | and use this to show tha ...
... (1) If a group G acts on a set S and s is in S, then the stablizer of s is Gs = {g ∈ G|gs = s}. The orbit of s is the set Os = {gs|g ∈ G}. (a) Prove that Gs is a subgroup of G. (b) Find a bijection between cosets of G/Gs and elements of Os . (c) Show that |Os | = |G| / |Gs | and use this to show tha ...
Chapter 1 The Basics
... a nice intuitive feel for what equivalence means: Since we can find a rotation relating any two given axes of rotations, rotations by the same angle about these two axes are equivalent. We remark that in the future we will consider smaller groups of rotations which may not contain the necessary rotat ...
... a nice intuitive feel for what equivalence means: Since we can find a rotation relating any two given axes of rotations, rotations by the same angle about these two axes are equivalent. We remark that in the future we will consider smaller groups of rotations which may not contain the necessary rotat ...
1 - Mu Alpha Theta
... 11. A symmetric matrix is a matrix M that has the property that MT = M. Only choice A satisfies this criterion. The answer is A. 12. The determinant is 2W - 4X, and the determinant is said to equal 10. if W+X = 8, then 4W + 4X = 32. Adding these two equations together shows that 6W = 42, or W = 7. S ...
... 11. A symmetric matrix is a matrix M that has the property that MT = M. Only choice A satisfies this criterion. The answer is A. 12. The determinant is 2W - 4X, and the determinant is said to equal 10. if W+X = 8, then 4W + 4X = 32. Adding these two equations together shows that 6W = 42, or W = 7. S ...
