MA 242 Section A2 Quiz 2
Spring 2016 Student Name
Show all your work for full credit.
1. (12 points) Compute the determinant of the matrix in two ways:
(a) by cofactor expansion
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MA242 Test 1
Arazyan, Spring 2016 February 25, 2016
1. (12 points) ROW reduce the matrix to reduced echelon form. Specify the row operations. Indicate When
you arrive at a matrix in echelon form.
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A: 1 0 3 4 N (2242 g .13 43
December 6, 2012
Theorem. If cfw_u1 , . . . , uk is an orthonormal basis for a subspace W , then
projW v = (vu1 )u1 + . . . + (vuk )uk .
U = u1
then projW v = UUT v.
The matrix UUT is called the projection matrix
December 4, 2012
Definition. A set of vectors cfw_v1 , v2 , . . . , vk is an orthogonal set if vi vj = 0 for all i 6= j.
Example 1. Consider the vectors
Theorem. Suppose that cfw_
October 25, 2012
More examples of vector spaces
Recall the definition of a vector space from last class:
Definition. A vector space V is a set of objects that are called vectors along with two
operationsvector addition and scalar multiplication. Th
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MA242 Quiz 1
Arazyan, Spring 2016 Student Name @431
I 0 POM); 1. Determine if the system is consistent. Do not completely solve the system.
6x2 = 5
4x3+x4 = 0
x1+6x2 +x3 +5x4 :3
x2 +5363 +4x4 = 0
[U WU t; 2. Write the matrix in reduced e
November 1, 2012
Bases for vector spaces and subspaces
Given a vector space or subspace V , we often find it convenient to express it as the span of
a few vectors. A basis for V is a spanning set that contains as few vectors as possible.
October 30, 2012
Subspaces associated to a matrix
There are three important subspaces associated to an m n matrix A. Let c1 , . . . , cn
represent the columns of A. That is,
These column vectors are vectors in Rm .
Let r1 , . . .
MA 242 Section A2 Quiz 4
Spring 2016 Student Name A45?
Show all your work for full credit.
1. Let u1:[l];u2= l ;y= l ,andW=Spancfw_ul,u2.
4 2 6
(a) (I 0 points) Verify that cfw_1,11, M2 is an orthogonal set, and then nd the orthogonal pro
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1. [12 points] Use Cramers rule to compute the value of x2 for the following system of equations.
x1 2x2 + x3 = 0
ZXZ 8X3 : 8 Y;
"496'1 + SXZ + 9X3 = 9
2. [12 points] Compute the adjugate of the given matrix, and then use it
MA242 /( . cfw_
Arazyan, Spring 2016 Student Name 2
Show all work for full credit.
1. ( 10 points] Use coordinate vectors to test the linear independence of the set of polynomials.
Explain your work.
(2 03, (3 t)2, 1 + 61: 5112 + t3
2. (9 points)
November 13, 2012
The dimension of a vector space
The number of elements in a basis of a vector space is an important quantity associated with
In order to be more precise, we need to distinguish between finite-dimensional vector spaces
The outer shell of the earth is composed of
individual plates that interact to produce:
Earthquakes, Mountains, Ocean basins,
Volcanoes, Ocean Trenches, etc.
Plate Tectonic Theory
This week we discuss one of the most important non linear
data structures in computing, trees.
Trees are indeed a breakthrough in data organization,
allowing us to implement a host of algorithms much faster
than when u