Intermediate Algebra Books a la Carte Edition PLUS MyLab Math (8th Edition)
8th Edition
ISBN: 9780134578507
Author: John Tobey Jr., Jeffrey Slater, Jenny Crawford, Jamie Blair
Publisher: PEARSON
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Chapter 6.2, Problem 28E
To determine
To calculate: The simplified form of the expression
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Students have asked these similar questions
Let
2
A =
4
3
-4
0
1
(a) Show that v =
eigenvalue.
()
is an eigenvector of A and find the corresponding
(b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a)
may be useful.
(c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces.
(d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.
(c) Let
6
0 0
A =
-10 4 8
5 1 2
(i) Find the characteristic polynomial of A and factorise it.
(ii) Determine all eigenvalues of A and find bases for the corresponding
eigenspaces.
(iii) Is A diagonalisable? Give reasons for your answer.
most 2, and let
Let P2 denote the vector space of polynomials of degree at
D: P2➡ P2
be the transformation that sends a polynomial p(t) = at² + bt+c in P2 to its derivative
p'(t)
2at+b, that is,
D(p) = p'.
(a) Prove that D is a linear transformation.
(b) Find a basis for the kernel ker(D) of the linear transformation D and compute its
nullity.
(c) Find a basis for the image im(D) of the linear transformation D and compute its
rank.
(d) Verify that the Rank-Nullity Theorem holds for the linear transformation D.
(e) Find the matrix representation of D in the standard basis (1,t, t2) of P2.
Chapter 6 Solutions
Intermediate Algebra Books a la Carte Edition PLUS MyLab Math (8th Edition)
Ch. 6.1 - Find the domain of each of the following rational...Ch. 6.1 - Find the domain of each of the following rational...Ch. 6.1 - Find the domain of each of the following rational...Ch. 6.1 - Prob. 4ECh. 6.1 - Simplify completely. − 18 x 4 y 12 x 2 y 6Ch. 6.1 - Simplify completely. − 7 x y 2 28 x 5 yCh. 6.1 - Prob. 7ECh. 6.1 - Simplify completely. 24 x 2 − 4 x 4 x 2 − 8 xCh. 6.1 - Simplify completely. 8 x 2 28 x 2 + 4 xCh. 6.1 - Simplify completely. 30 x 2 6 x 2 + 18 x
Ch. 6.1 - Simplify completely.
11.
Ch. 6.1 - Simplify completely. 6 m 2 n 4 + 2 m n 3 4 m n 2 −...Ch. 6.1 - Simplify completely.
13.
Ch. 6.1 - Simplify completely. 6 x 2 − 15 x 3 xCh. 6.1 - Simplify completely.
15.
Ch. 6.1 - Simplify completely. x + 2 7 x 2 − 28Ch. 6.1 - Simplify completely.
17.
Ch. 6.1 - Simplify completely.
18.
Ch. 6.1 - Simplify completely 2 y 2 + y − 10 4 − y 2Ch. 6.1 - Simplify completely.
20.
Ch. 6.1 - Multiply.
21.
Ch. 6.1 - Multiply. 24 x 4 y 2 − 12 x 5 y ⋅ 8 x 3 30 x 2 yCh. 6.1 - Multiply. 3 a 2 a 2 + 4 a + 4 ⋅ a 2 − 4 3 aCh. 6.1 - Multiply.
24.
Ch. 6.1 - Multiply.
25.
Ch. 6.1 - Multiply.
26.
Ch. 6.1 - Multiply. x 2 − 3 x y − 10 y 2 x + y ⋅ x 2 + 7 x y...Ch. 6.1 - Multiply.
28.
Ch. 6.1 - Multiply. y 2 − y − 12 2 y 2 + y − 1 ⋅ 2 x y 2 + 7...Ch. 6.1 - Multiply.
30.
Ch. 6.1 - Multiply.
31.
Ch. 6.1 - Prob. 32ECh. 6.1 - Divide. 2 m n − m 15 m 3 ÷ 2 n − 1 3 m 2Ch. 6.1 - Prob. 34ECh. 6.1 - Divide.
35.
Ch. 6.1 - Divide. a 2 − 3 a a 2 − 9 ÷ a 3 − a 2 4 a 2 − a −...Ch. 6.1 - Divide. x 2 − x y − 6 y 2 x 2 + 2 ÷ ( x 2 + 2 x y...Ch. 6.1 - Divide. x 2 − 5 x + 4 2 x − 8 ÷ ( 3 x 2 − 3 x )Ch. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - Perform the operation indicated When no operation...Ch. 6.1 - Prob. 44ECh. 6.1 - Perform the operation indicated When no operation...Ch. 6.1 - Prob. 46ECh. 6.1 - Perform the operation indicated When no operation...Ch. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Tropical Fish The total number of fish will depend...Ch. 6.1 - Prob. 52ECh. 6.1 - Prob. 53ECh. 6.1 - Prob. 54ECh. 6.1 - Tropical Fish The total number of fish will depend...Ch. 6.1 - Tropical Fish The total number of fish will depend...Ch. 6.1 - 57. [2.6.3] Solve.
Ch. 6.1 - 58. [5.1.6] Multiply.
Ch. 6.1 - 59. [1.2.2] Motorcyclist Deaths Between 2008 and...Ch. 6.1 - Prob. 1QQCh. 6.1 - Prob. 2QQCh. 6.1 - Prob. 3QQCh. 6.1 - Prob. 4QQCh. 6.2 - Verbal and Writing Skills, Exercises 1 and 2
1....Ch. 6.2 - Prob. 2ECh. 6.2 - Find the LCD. 3 x − 1 , 4 x 2 − 2 x + 1Ch. 6.2 - Prob. 4ECh. 6.2 - Find the LCD.
5.
Ch. 6.2 - Prob. 6ECh. 6.2 - Find the LCD. 3 x ( 2 x + 5 ) 3 , x − 2 ( x + 1...Ch. 6.2 - Prob. 8ECh. 6.2 - Find the LCD. 2 y 2 x 2 + x , 11 x y 15 x 2 − x...Ch. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Add or subtract and simplify your answers.
13.
Ch. 6.2 - Prob. 14ECh. 6.2 - Add or subtract and simplify your answers. 3 x 2 −...Ch. 6.2 - Prob. 16ECh. 6.2 - Add or subtract and simplify your answers.
17.
Ch. 6.2 - Prob. 18ECh. 6.2 - Add or subtract and simplify your answers. − 5 y y...Ch. 6.2 - Prob. 20ECh. 6.2 - Add or subtract and simplify your answers.
21.
Ch. 6.2 - Prob. 22ECh. 6.2 - Add or subtract and simplify your answers. 5 x − 4...Ch. 6.2 - Prob. 24ECh. 6.2 - Add or subtract and simplify your answers.
25.
Ch. 6.2 - Add or subtract and simplify your answers.
26.
Ch. 6.2 - Add or subtract and simplify your answers. 4 y y 2...Ch. 6.2 - Prob. 28ECh. 6.2 - Add or subtract and simplify your answers. a + 2 +...Ch. 6.2 - Prob. 30ECh. 6.2 - 31. Artificial Lung If an artificial lung company...Ch. 6.2 - Prob. 32ECh. 6.2 - Prob. 33ECh. 6.2 - 34. Artificial Heart Determine the daily profit of...Ch. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - 37. [2.5.1] Purchase Price of Automobiles Jamie,...Ch. 6.2 - Prob. 38ECh. 6.2 - Prob. 1QQCh. 6.2 - Prob. 2QQCh. 6.2 - Prob. 3QQCh. 6.2 - Prob. 4QQCh. 6.3 - Simplify the complex fractions by any method.
1.
Ch. 6.3 - Prob. 2ECh. 6.3 - Simplify the complex fractions by any method. − 4...Ch. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - Simplify the complex fractions by any method. 3 2...Ch. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - Simplify the complex fractions by any method.
19....Ch. 6.3 - Prob. 20ECh. 6.3 - Prob. 21ECh. 6.3 - Prob. 22ECh. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - Prob. 1QQCh. 6.3 - Prob. 2QQCh. 6.3 - Prob. 3QQCh. 6.3 - Prob. 4QQCh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 2ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 4ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 9ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 14ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 16ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 18ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 22ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 24ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 28ECh. 6.4 - Verbal and Writing Skills In what situations will...Ch. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Factor completely. [5.7.1] 2 x 2 + 20 x + 50Ch. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Factor completely. [5.2.2] Divide. ( 2 x 3 − 3 x 2...Ch. 6.4 - Prob. 1QQCh. 6.4 - Prob. 2QQCh. 6.4 - Prob. 3QQCh. 6.4 - Prob. 4QQCh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Solve for the indicated variable.
3.
Ch. 6.5 - Solve for the indicated variable 1 f = 1 a + 1 b ;...Ch. 6.5 - Solve for the indicated variable. V l h = w ; ...Ch. 6.5 - Solve for the indicated variable r = I p t ; for...Ch. 6.5 - Solve for the indicated variable.
7.
Ch. 6.5 - Solve for the indicated variable.
8.
Ch. 6.5 - Solve for the indicated variable r 3 V = 3 4 π ; ...Ch. 6.5 - Solve for the indicated variable
10.
Ch. 6.5 - Solve for the indicated variable. F = k q 1 q 2 r...Ch. 6.5 - Solve for the indicated variable. F = k q 1 q 2 r...Ch. 6.5 - Solve for the indicated variable. Q R 1 S 1 = Q R...Ch. 6.5 - Solve for the indicated variable. Q R 1 S 1 = Q R...Ch. 6.5 - Prob. 15ECh. 6.5 - Prob. 16ECh. 6.5 - Prob. 17ECh. 6.5 - Prob. 18ECh. 6.5 - Prob. 19ECh. 6.5 - Prob. 20ECh. 6.5 - Prob. 21ECh. 6.5 - Prob. 22ECh. 6.5 - Prob. 23ECh. 6.5 - Prob. 24ECh. 6.5 - Prob. 25ECh. 6.5 - Prob. 26ECh. 6.5 - Prob. 27ECh. 6.5 - Prob. 28ECh. 6.5 - Prob. 29ECh. 6.5 - Prob. 30ECh. 6.5 - Map Scale On a map of Nigeria, the cities of Benin...Ch. 6.5 - Prob. 32ECh. 6.5 - Prob. 33ECh. 6.5 - Prob. 34ECh. 6.5 - In exercises 35-50, round your answers to the...Ch. 6.5 - Prob. 36ECh. 6.5 - Prob. 37ECh. 6.5 - Prob. 38ECh. 6.5 - Prob. 39ECh. 6.5 - Prob. 40ECh. 6.5 - Prob. 41ECh. 6.5 - Prob. 42ECh. 6.5 - Prob. 43ECh. 6.5 - Prob. 44ECh. 6.5 - Prob. 45ECh. 6.5 - Prob. 46ECh. 6.5 - Prob. 47ECh. 6.5 - Prob. 48ECh. 6.5 - In exercises 35-50, round your answers to the...Ch. 6.5 - Prob. 50ECh. 6.5 - Prob. 51ECh. 6.5 - Prob. 52ECh. 6.5 - Prob. 53ECh. 6.5 - Prob. 54ECh. 6.5 - Prob. 55ECh. 6.5 - Prob. 56ECh. 6.5 - Prob. 1QQCh. 6.5 - Prob. 2QQCh. 6.5 - Prob. 3QQCh. 6.5 - Prob. 4QQCh. 6 - Simplify.
1.
Ch. 6 - Prob. 2RPCh. 6 - Prob. 3RPCh. 6 - Prob. 4RPCh. 6 - Prob. 5RPCh. 6 - Prob. 6RPCh. 6 - Prob. 7RPCh. 6 - Prob. 8RPCh. 6 - Simplify.
9.
Ch. 6 - Prob. 10RPCh. 6 - Prob. 11RPCh. 6 - Prob. 12RPCh. 6 - Prob. 13RPCh. 6 - Prob. 14RPCh. 6 - Prob. 15RPCh. 6 - Prob. 16RPCh. 6 - Prob. 17RPCh. 6 - Prob. 18RPCh. 6 - Prob. 19RPCh. 6 - Prob. 20RPCh. 6 - Prob. 21RPCh. 6 - Prob. 22RPCh. 6 - Prob. 23RPCh. 6 - Prob. 24RPCh. 6 - Prob. 25RPCh. 6 - Prob. 26RPCh. 6 - Prob. 27RPCh. 6 - Prob. 28RPCh. 6 - Prob. 29RPCh. 6 - Prob. 30RPCh. 6 - Prob. 31RPCh. 6 - Prob. 32RPCh. 6 - Prob. 33RPCh. 6 - Prob. 34RPCh. 6 - Prob. 35RPCh. 6 - Prob. 36RPCh. 6 - Prob. 37RPCh. 6 - Prob. 38RPCh. 6 - Prob. 39RPCh. 6 - Prob. 40RPCh. 6 - Prob. 41RPCh. 6 - Prob. 42RPCh. 6 - Prob. 43RPCh. 6 - Prob. 44RPCh. 6 - Prob. 45RPCh. 6 - Prob. 46RPCh. 6 - Prob. 47RPCh. 6 - Prob. 48RPCh. 6 - Solve the following exercises. If necessary, round...Ch. 6 - Prob. 50RPCh. 6 - Solve the following exercises. If necessary, round...Ch. 6 - Prob. 52RPCh. 6 - Prob. 53RPCh. 6 - Prob. 54RPCh. 6 - Prob. 55RPCh. 6 - Prob. 1TCh. 6 - Prob. 2TCh. 6 - Prob. 3TCh. 6 - Prob. 4TCh. 6 - Prob. 5TCh. 6 - Prob. 6TCh. 6 - Prob. 7TCh. 6 - Prob. 8TCh. 6 - Prob. 9TCh. 6 - Prob. 10TCh. 6 - Prob. 11TCh. 6 - Prob. 12TCh. 6 - Prob. 13TCh. 6 - Prob. 14TCh. 6 - Prob. 15TCh. 6 - Prob. 16TCh. 6 - Prob. 1CTCh. 6 - Prob. 2CTCh. 6 - Prob. 3CTCh. 6 - Prob. 4CTCh. 6 - Prob. 5CTCh. 6 - Prob. 6CTCh. 6 - Prob. 7CTCh. 6 - Prob. 8CTCh. 6 - Prob. 9CTCh. 6 - Prob. 10CTCh. 6 - Prob. 11CTCh. 6 - Prob. 12CTCh. 6 - Prob. 13CTCh. 6 - Prob. 14CTCh. 6 - Prob. 15CTCh. 6 - Prob. 16CTCh. 6 - Prob. 17CTCh. 6 - Prob. 18CTCh. 6 - Prob. 19CTCh. 6 - Prob. 20CTCh. 6 - Prob. 21CTCh. 6 - Prob. 22CTCh. 6 - Prob. 23CTCh. 6 - Prob. 24CTCh. 6 - Prob. 25CTCh. 6 - Prob. 26CTCh. 6 - Prob. 27CTCh. 6 - Prob. 28CTCh. 6 - Prob. 29CTCh. 6 - The mayor of Chicago decided that in the coming...
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