Explanation Given: The functions are f ( x ) = x 2 and g ( x ) = ( x + 2 ) 2 + 4 . Graph: Consider the following function: f ( x ) = x 2 For x = − 2 , Substitute − 2 for x . f ( − 2 ) = ( − 2 ) 2 = 4 For x = − 1 , Substitute − 1 for x . f ( − 1 ) = ( − 1 ) 2 = 1 For x = 0 , Substitute 0 for x . f ( 0 ) = ( 0 ) 2 = 0 For x = 1 , Substitute 1 for x . f ( 1 ) = ( 1 ) 2 = 1 For x = 2 , Substitute 2 for x . f ( 2 ) = ( 2 ) 2 = 4 Construct a table, for various values of x , for the function, f ( x ) = x 2 . x f ( x ) = x 2 − 2 4 − 1 1 0 0 1 1 2 4 Consider the function, g ( x ) = ( x + 2 ) 2 + 4 . For x = − 2 , Substitute − 2 for x . g ( − 2 ) = ( − 2 + 2 ) 2 + 4 = ( 0 ) 2 + 4 = 4 For x = − 1 , Substitute − 1 for x

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ISBN: 9780135909942

Author: TOBEY/SLATER

Publisher: PEARSON

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Chapter 10, Problem 20RP

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To graph: The functions f(x)=x2 and g(x)=(x+2)2+4 on one coordinate plane.

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Chapter 10, Problem 19RP

Chapter 10, Problem 21RP

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Question 3 over a field K. In this question, MË(K) denotes the set of n × n matrices (a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is equivalent to A-¹? Justify your answer. (b) Let B be given by 8 B = 0 7 7 0 -7 7 Working over the field F2 with 2 elements, compute the rank of B as an element of M2(F2). (c) Let 1 C -1 1 [4] [6] and consider C as an element of M3(Q). Determine the minimal polynomial mc(x) and hence, or otherwise, show that C can not be diagonalised. [7] (d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write down all the eigenvalues. Show your working. [8]

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Chapter 10 Solutions

INTERMEDIATE ALGEBRA - 18 WEEK MML CODE

Ch. 10.1 - For the function f ( x ) = 3 x − 5 , find the...Ch. 10.1 - For the function , find the following. 2. Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - For the function , find the following. 7. Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

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To graph: The functions f ( x ) = x 2 and g ( x ) = ( x + 2 ) 2 + 4 on one coordinate plane.

Solution Summary: The author explains the functions f(x)=x, and g left (x+2)2+4 on one coordinate plane.

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To graph: The functions f(x)=x2 and g(x)=(x+2)2+4 on one coordinate plane.

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Chapter 10 Solutions