
Contemporary Abstract Algebra
9th Edition
ISBN: 9781305657960
Author: Joseph Gallian
Publisher: Cengage Learning
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It is given that E4E3E2E1A=⎡⎣⎢⎢⎢−1002−40488⎤⎦⎥⎥⎥.
Here the matrices E4, E3, E2, and, E1 are:
E1=⎡⎣⎢⎢⎢100010008⎤⎦⎥⎥⎥E2=⎡⎣⎢⎢⎢100010−501⎤⎦⎥⎥⎥E3=⎡⎣⎢⎢⎢1000−10001⎤⎦⎥⎥⎥E4=⎡⎣⎢⎢⎢001010100⎤⎦⎥⎥⎥
What is the determinant of A?
Use the graph of the function y = f(x) below to answer the questions.
4
3-
2+
1
-5 -4
-3
-2
-1
3
-1+
-2+
-3+
-4-
-5+
(a) Isf (3) negative?
Yes No
(b) For which value(s) of x is f(x) = 0?
If there is more than one value, separate them with commas.
(c) For which value(s) of x is f(x) ≤0?
Write your answer using interval notation.
Name:
Date:
Transformations of Quadratic Functions
y=a(x-h)²+k
Describe all transformations for each quadratic function.
1.
2.
-2
2
-4
2
2
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