FUNCTIONS AND CHANGE COMBO
6th Edition
ISBN: 9781337801287
Author: Crauder
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter P, Problem 2E
Pet Owners According to the Humane Society, in 2015,
least one pet, and
Bureau tells us that there were
owned at least two pets? Report your answer in millions rounded to two places.
Expert Solution & Answer
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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 P Solutions
FUNCTIONS AND CHANGE COMBO
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Ch. P - Pay Raise You receive a raise in your hourly pay...Ch. P - Heart Disease In a certain country, the number of...Ch. P - Trade Discount Often retailers sell merchandise at...Ch. P - Series Discount This is a continuation of Exercise...Ch. P - Present Value Present value is the amount of money...Ch. P - Future Value Business and finance texts refer to...Ch. P - The Rule of 72 This is a continuation of Exercise...Ch. P - The Truth in Lending Act Many lending agencies...Ch. P - The Size of the Earth The radius of the Earth is...Ch. P - When the Radius Increases a. A rope is wrapped...Ch. P - The Length of Earths Orbit The Earth is...Ch. P - Prob. 20ECh. P - Prob. 21ECh. P - Prob. 22ECh. P - Prob. 23ECh. P - Lean Body Weight in Males A persons lean body...Ch. P - Lean Body Weight in Females This is a continuation...Ch. P - Mannings Equation Hydrologists sometimes use...Ch. P - Relativistic Length A rocket ship travelling near...Ch. P - Equity in a Home When you purchase a home by...Ch. P - The Advantage Cash Card At the student union on a...Ch. P - Prob. 1SBECh. P - Prob. 2SBECh. P - Prob. 3SBECh. P - Basic Calculations 7.61.79.2Ch. P - Parenthesis and Grouping 7.3-6.82.5+1.8Ch. P - Prob. 6SBECh. P - Parentheses and Grouping 6+e+13Ch. P - Parentheses and Grouping -e+eCh. P - Prob. 9SBECh. P - Prob. 10SBECh. P - Prob. 11SBECh. P - Prob. 12SBECh. P - Prob. 13SBECh. P - Prob. 14SBECh. P - Prob. 15SBECh. P - Prob. 16SBECh. P - Arithmetic In Exercises S-16 through S-20, perform...Ch. P - Prob. 18SBECh. P - Prob. 19SBECh. P - Prob. 20SBECh. P - Prob. 21SBECh. P - Prob. 22SBECh. P - Prob. 23SBECh. P - Prob. 24SBECh. P - Prob. 25SBECh. P - Prob. 26SBECh. P - Prob. 27SBECh. P - Prob. 28SBECh. P - Prob. 29SBECh. P - Evaluating Formulas In Exercises S-21 through...Ch. P - Lending Money For a certain loan, the interest I...Ch. P - Monthly Payment For a certain instalment loan, the...Ch. P - Prob. 33SBECh. P - A Skydiver When a skydiver jumps from an airplane,...Ch. P - Future Value In certain savings scenarios, the...Ch. P - A Population of Deer The number N of deer in a...Ch. P - Prob. 37SBECh. P - Getting Three Sixes If we roll n fair dice, then...Ch. P - Prob. 1CRCh. P - Prob. 2CRCh. P - Prob. 3CRCh. P - Prob. 4CRCh. P - Keplers Third Law According to Keplers third law...Ch. P - Traffic Signal Traffic engineers study how long...
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- (c) Let A = -1 3 -4 12 3 3 -9 (i) Find bases for row(A), col(A) and N(A). (ii) Determine the rank and nullity of A, and verify that the Rank-Nullity Theorem holds for the above matrix A.arrow_forward-(0)-(0)-(0) X1 = x2 = x3 = 1 (a) Show that the vectors X1, X2, X3 form a basis for R³. y= (b) Find the coordinate vector [y] B of y in the basis B = (x1, x2, x3).arrow_forwardLet A 1 - 13 (1³ ³) 3). (i) Compute A2, A3, A4. (ii) Show that A is invertible and find A-¹.arrow_forward
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