Pearson eText Elementary and Intermediate Algebra: Concepts and Applications -- Instant Access (Pearson+)
7th Edition
ISBN: 9780137361847
Author: Marvin Bittinger, David Ellenbogen
Publisher: PEARSON+
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Chapter R.1, Problem 31ES
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Consider the function f(x)=x³ + 2x² − 3
(a) Graph the function.
(b) What are the x- and y-intercepts of the graph?
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.
Chapter R Solutions
Pearson eText Elementary and Intermediate Algebra: Concepts and Applications -- Instant Access (Pearson+)
Ch. R.1 - Prob. 1YTCh. R.1 - Prob. 2YTCh. R.1 - Prob. 3YTCh. R.1 - Prob. 4YTCh. R.1 - Prob. 5YTCh. R.1 - Prob. 6YTCh. R.1 - Prob. 7YTCh. R.1 - Prob. 8YTCh. R.1 - Prob. 9YTCh. R.1 - Prob. 1ES
Ch. R.1 - Prob. 2ESCh. R.1 - Prob. 3ESCh. R.1 - Prob. 4ESCh. R.1 - Prob. 5ESCh. R.1 - Prob. 6ESCh. R.1 - Prob. 7ESCh. R.1 - Prob. 8ESCh. R.1 - Prob. 9ESCh. R.1 - Prob. 10ESCh. R.1 - Prob. 11ESCh. R.1 - Prob. 12ESCh. R.1 - Prob. 13ESCh. R.1 - Prob. 14ESCh. R.1 - Prob. 15ESCh. R.1 - Prob. 16ESCh. R.1 - Prob. 17ESCh. R.1 - Prob. 18ESCh. R.1 - Prob. 19ESCh. R.1 - Prob. 20ESCh. R.1 - Prob. 21ESCh. R.1 - Prob. 22ESCh. R.1 - Prob. 23ESCh. R.1 - Prob. 24ESCh. R.1 - Prob. 25ESCh. R.1 - Prob. 26ESCh. R.1 - Prob. 27ESCh. R.1 - Prob. 28ESCh. R.1 - Prob. 29ESCh. R.1 - Prob. 30ESCh. R.1 - Prob. 31ESCh. R.1 - Prob. 32ESCh. R.1 - Prob. 33ESCh. R.1 - Prob. 34ESCh. R.1 - Prob. 35ESCh. R.1 - Prob. 36ESCh. R.1 - Prob. 37ESCh. R.1 - Prob. 38ESCh. R.1 - Prob. 39ESCh. R.1 - Prob. 40ESCh. R.1 - Prob. 41ESCh. R.1 - Prob. 42ESCh. R.1 - Prob. 43ESCh. R.1 - Prob. 44ESCh. R.1 - Prob. 45ESCh. R.1 - Prob. 46ESCh. R.1 - Prob. 47ESCh. R.1 - Prob. 48ESCh. R.1 - Prob. 49ESCh. R.1 - Prob. 50ESCh. R.1 - Prob. 51ESCh. R.1 - Prob. 52ESCh. R.1 - Prob. 53ESCh. R.1 - Prob. 54ESCh. R.1 - Prob. 55ESCh. R.1 - Prob. 56ESCh. R.1 - Prob. 57ESCh. R.1 - Prob. 58ESCh. R.1 - Prob. 59ESCh. R.1 - Prob. 60ESCh. R.1 - Prob. 61ESCh. R.1 - Prob. 62ESCh. R.1 - Prob. 63ESCh. R.1 - Prob. 64ESCh. R.1 - Prob. 65ESCh. R.1 - Prob. 66ESCh. R.1 - Prob. 67ESCh. R.1 - Prob. 68ESCh. R.1 - Prob. 69ESCh. R.1 - Prob. 70ESCh. R.1 - Prob. 71ESCh. R.1 - Prob. 72ESCh. R.1 - Prob. 73ESCh. R.1 - Prob. 74ESCh. R.1 - Prob. 75ESCh. R.1 - Prob. 76ESCh. R.1 - Prob. 77ESCh. R.1 - Prob. 78ESCh. R.1 - Prob. 79ESCh. R.1 - Prob. 80ESCh. R.1 - Prob. 81ESCh. R.1 - Prob. 82ESCh. R.1 - Prob. 83ESCh. R.1 - Prob. 84ESCh. R.1 - Prob. 85ESCh. R.1 - Prob. 86ESCh. R.1 - Prob. 87ESCh. R.1 - Prob. 88ESCh. R.1 - Prob. 89ESCh. R.1 - Translate each problem to an equation. Do not...Ch. R.1 - Prob. 91ESCh. R.1 - Prob. 92ESCh. R.1 - Prob. 93ESCh. R.2 - Prob. 1YTCh. R.2 - Prob. 2YTCh. R.2 - Prob. 3YTCh. R.2 - Prob. 4YTCh. R.2 - Prob. 5YTCh. R.2 - Prob. 6YTCh. R.2 - Prob. 7YTCh. R.2 - Prob. 8YTCh. R.2 - Prob. 1ESCh. R.2 - Prob. 2ESCh. R.2 - Prob. 3ESCh. R.2 - Prob. 4ESCh. R.2 - Prob. 5ESCh. R.2 - Prob. 6ESCh. R.2 - Prob. 7ESCh. R.2 - Prob. 8ESCh. R.2 - Prob. 9ESCh. R.2 - Prob. 10ESCh. R.2 - Prob. 11ESCh. R.2 - Prob. 12ESCh. R.2 - Prob. 13ESCh. R.2 - Prob. 14ESCh. R.2 - Prob. 15ESCh. R.2 - Prob. 16ESCh. R.2 - Prob. 17ESCh. R.2 - Prob. 18ESCh. R.2 - Prob. 19ESCh. R.2 - Prob. 20ESCh. R.2 - Prob. 21ESCh. R.2 - Prob. 22ESCh. R.2 - Prob. 23ESCh. R.2 - Prob. 24ESCh. R.2 - Prob. 25ESCh. R.2 - Prob. 26ESCh. R.2 - Prob. 27ESCh. R.2 - Prob. 28ESCh. R.2 - Prob. 29ESCh. R.2 - Prob. 30ESCh. R.2 - Prob. 31ESCh. R.2 - Prob. 32ESCh. R.2 - Prob. 33ESCh. R.2 - Prob. 34ESCh. R.2 - Prob. 35ESCh. R.2 - Prob. 36ESCh. R.2 - Prob. 37ESCh. R.2 - Prob. 38ESCh. R.2 - Prob. 39ESCh. R.2 - Prob. 40ESCh. R.2 - Prob. 41ESCh. R.2 - Prob. 42ESCh. R.2 - Prob. 43ESCh. R.2 - Prob. 44ESCh. R.2 - Prob. 45ESCh. R.2 - Prob. 46ESCh. R.2 - Prob. 47ESCh. R.2 - Prob. 48ESCh. R.2 - Prob. 49ESCh. R.2 - Prob. 50ESCh. R.2 - Prob. 51ESCh. R.2 - Prob. 52ESCh. R.2 - Prob. 53ESCh. R.2 - Prob. 54ESCh. R.2 - Prob. 55ESCh. R.2 - Prob. 56ESCh. R.2 - Prob. 57ESCh. R.2 - Prob. 58ESCh. R.2 - Prob. 59ESCh. R.2 - Prob. 60ESCh. R.2 - Prob. 61ESCh. R.2 - Prob. 62ESCh. R.2 - Prob. 63ESCh. R.2 - Prob. 64ESCh. R.2 - Prob. 65ESCh. R.2 - Prob. 66ESCh. R.2 - Prob. 67ESCh. R.2 - Prob. 68ESCh. R.2 - Prob. 69ESCh. R.2 - Prob. 70ESCh. R.2 - Prob. 71ESCh. R.2 - Prob. 72ESCh. R.3 - Prob. 1YTCh. R.3 - Prob. 2YTCh. R.3 - Prob. 3YTCh. R.3 - Prob. 4YTCh. R.3 - Prob. 5YTCh. R.3 - Prob. 6YTCh. R.3 - Prob. 7YTCh. R.3 - Prob. 8YTCh. R.3 - Prob. 1ESCh. R.3 - Prob. 2ESCh. R.3 - Prob. 3ESCh. R.3 - Prob. 4ESCh. R.3 - Prob. 5ESCh. R.3 - Prob. 6ESCh. R.3 - Prob. 7ESCh. R.3 - Prob. 8ESCh. R.3 - Prob. 9ESCh. R.3 - Prob. 10ESCh. R.3 - Prob. 11ESCh. R.3 - Prob. 12ESCh. R.3 - Prob. 13ESCh. R.3 - Prob. 14ESCh. R.3 - Prob. 15ESCh. R.3 - Prob. 16ESCh. R.3 - Prob. 17ESCh. R.3 - Prob. 18ESCh. R.3 - Prob. 19ESCh. R.3 - Prob. 20ESCh. R.3 - Prob. 21ESCh. R.3 - Prob. 22ESCh. R.3 - Prob. 23ESCh. R.3 - Prob. 24ESCh. R.3 - Prob. 25ESCh. R.3 - Prob. 26ESCh. R.3 - Prob. 27ESCh. R.3 - Prob. 28ESCh. R.3 - Prob. 29ESCh. R.3 - Prob. 30ESCh. R.3 - Prob. 31ESCh. R.3 - Prob. 32ESCh. R.3 - Prob. 33ESCh. R.3 - Prob. 34ESCh. R.3 - Prob. 35ESCh. R.3 - Prob. 36ESCh. R.3 - Prob. 37ESCh. R.3 - Prob. 38ESCh. R.3 - Prob. 39ESCh. R.3 - Prob. 40ESCh. R.3 - Prob. 41ESCh. R.3 - Prob. 42ESCh. R.3 - Prob. 43ESCh. R.3 - Prob. 44ESCh. R.3 - Prob. 45ESCh. R.3 - Prob. 46ESCh. R.4 - Prob. 1YTCh. R.4 - Prob. 2YTCh. R.4 - 3. Combine like terms:
.
Write the answer in...Ch. R.4 - Prob. 4YTCh. R.4 - Prob. 5YTCh. R.4 - Prob. 6YTCh. R.4 - Prob. 7YTCh. R.4 - Prob. 8YTCh. R.4 - Prob. 9YTCh. R.4 - Prob. 10YTCh. R.4 - Prob. 11YTCh. R.4 - Prob. 12YTCh. R.4 - Prob. 1ESCh. R.4 - Prob. 2ESCh. R.4 - Prob. 3ESCh. R.4 - Prob. 4ESCh. R.4 - Prob. 5ESCh. R.4 - Prob. 6ESCh. R.4 - Prob. 7ESCh. R.4 - Prob. 8ESCh. R.4 - Prob. 9ESCh. R.4 - Prob. 10ESCh. R.4 - Prob. 11ESCh. R.4 - Prob. 12ESCh. R.4 - Prob. 13ESCh. R.4 - Prob. 14ESCh. R.4 - Prob. 15ESCh. R.4 - Prob. 16ESCh. R.4 - Prob. 17ESCh. R.4 - Prob. 18ESCh. R.4 - Prob. 19ESCh. R.4 - Prob. 20ESCh. R.4 - Prob. 21ESCh. R.4 - Prob. 22ESCh. R.4 - Prob. 23ESCh. R.4 - Prob. 24ESCh. R.4 - Prob. 25ESCh. R.4 - Prob. 26ESCh. R.4 - Identify the terms of each polynomial.
27.
Ch. R.4 - Identify the terms of each polynomial.
28.
Ch. R.4 - Determine the coefficient and the degree of each...Ch. R.4 - Prob. 30ESCh. R.4 - Determine the coefficient and the degree of each...Ch. R.4 - Determine the coefficient and the degree of each...Ch. R.4 - Prob. 33ESCh. R.4 - Prob. 34ESCh. R.4 - Prob. 35ESCh. R.4 - Prob. 36ESCh. R.4 - Prob. 37ESCh. R.4 - Prob. 38ESCh. R.4 - Prob. 39ESCh. R.4 - Prob. 40ESCh. R.4 - Prob. 41ESCh. R.4 - Prob. 42ESCh. R.4 - Prob. 43ESCh. R.4 - Prob. 44ESCh. R.4 - Prob. 45ESCh. R.4 - Prob. 46ESCh. R.4 - Prob. 47ESCh. R.4 - Prob. 48ESCh. R.4 - Prob. 49ESCh. R.4 - Prob. 50ESCh. R.4 - Prob. 51ESCh. R.4 - Prob. 52ESCh. R.4 - Prob. 53ESCh. R.4 - Prob. 54ESCh. R.4 - Prob. 55ESCh. R.4 - Prob. 56ESCh. R.4 - Prob. 57ESCh. R.4 - Prob. 58ESCh. R.4 - Prob. 59ESCh. R.4 - Prob. 60ESCh. R.4 - Prob. 61ESCh. R.4 - Prob. 62ESCh. R.4 - Prob. 63ESCh. R.4 - Prob. 64ESCh. R.4 - Prob. 65ESCh. R.4 - Prob. 66ESCh. R.4 - Prob. 67ESCh. R.4 - Prob. 68ESCh. R.4 - Prob. 69ESCh. R.4 - Prob. 70ESCh. R.4 - Prob. 71ESCh. R.4 - Prob. 72ESCh. R.5 - Prob. 1YTCh. R.5 - Prob. 2YTCh. R.5 - Prob. 3YTCh. R.5 - Prob. 4YTCh. R.5 - Prob. 5YTCh. R.5 - Prob. 6YTCh. R.5 - Prob. 7YTCh. R.5 - Prob. 8YTCh. R.5 - Prob. 9YTCh. R.5 - Prob. 1ESCh. R.5 - Prob. 2ESCh. R.5 - Prob. 3ESCh. R.5 - Prob. 4ESCh. R.5 - Prob. 5ESCh. R.5 - Prob. 6ESCh. R.5 - Prob. 7ESCh. R.5 - Prob. 8ESCh. R.5 - Prob. 9ESCh. R.5 - Prob. 10ESCh. R.5 - Prob. 11ESCh. R.5 - Prob. 12ESCh. R.5 - Prob. 13ESCh. R.5 - Prob. 14ESCh. R.5 - Prob. 15ESCh. R.5 - Prob. 16ESCh. R.5 - Prob. 17ESCh. R.5 - Prob. 18ESCh. R.5 - Prob. 19ESCh. R.5 - Prob. 20ESCh. R.5 - Prob. 21ESCh. R.5 - Prob. 22ESCh. R.5 - Prob. 23ESCh. R.5 - Prob. 24ESCh. R.5 - Prob. 25ESCh. R.5 - Prob. 26ESCh. R.5 - Prob. 27ESCh. R.5 - Prob. 28ESCh. R.5 - Prob. 29ESCh. R.5 - Prob. 30ESCh. R.5 - Prob. 31ESCh. R.5 - Prob. 32ESCh. R.5 - Prob. 33ESCh. R.5 - Prob. 34ESCh. R.5 - Prob. 35ESCh. R.5 - Prob. 36ESCh. R.5 - Prob. 37ESCh. R.5 - Prob. 38ESCh. R.5 - Prob. 39ESCh. R.5 - Prob. 40ESCh. R.5 - Prob. 41ESCh. R.5 - Prob. 42ESCh. R.5 - Prob. 43ESCh. R.5 - Prob. 44ESCh. R.5 - Prob. 45ESCh. R.5 - Prob. 46ESCh. R.5 - Prob. 47ESCh. R.5 - 48. Page Numbers. The product of the page numbers...Ch. R.5 - Prob. 49ESCh. R.5 - Prob. 50ESCh. R.6 - Prob. 1YTCh. R.6 - Prob. 2YTCh. R.6 - Prob. 3YTCh. R.6 - Prob. 4YTCh. R.6 - Prob. 5YTCh. R.6 - Prob. 6YTCh. R.6 - Prob. 7YTCh. R.6 - Prob. 8YTCh. R.6 - Prob. 9YTCh. R.6 - Prob. 10YTCh. R.6 - Prob. 11YTCh. R.6 - Prob. 12YTCh. R.6 - Prob. 1ESCh. R.6 - Prob. 2ESCh. R.6 - Prob. 3ESCh. R.6 - Prob. 4ESCh. R.6 - Prob. 5ESCh. R.6 - Prob. 6ESCh. R.6 - Prob. 7ESCh. R.6 - Prob. 8ESCh. R.6 - Prob. 9ESCh. R.6 - Prob. 10ESCh. R.6 - Prob. 11ESCh. R.6 - Prob. 12ESCh. R.6 - Prob. 13ESCh. R.6 - Prob. 14ESCh. R.6 - Prob. 15ESCh. R.6 - Prob. 16ESCh. R.6 - Prob. 17ESCh. R.6 - Prob. 18ESCh. R.6 - Prob. 19ESCh. R.6 - Prob. 20ESCh. R.6 - Prob. 21ESCh. R.6 - Prob. 22ESCh. R.6 - Prob. 23ESCh. R.6 - Prob. 24ESCh. R.6 - Prob. 25ESCh. R.6 - Prob. 26ESCh. R.6 - Prob. 27ESCh. R.6 - Prob. 28ESCh. R.6 - Prob. 29ESCh. R.6 - Prob. 30ESCh. R.6 - Prob. 31ESCh. R.6 - Prob. 32ESCh. R.6 - Prob. 33ESCh. R.6 - Prob. 34ESCh. R.6 - Prob. 35ESCh. R.6 - Prob. 36ESCh. R.6 - Prob. 37ESCh. R.6 - Prob. 38ESCh. R.6 - Prob. 39ESCh. R.6 - Prob. 40ESCh. R.6 - Prob. 41ESCh. R.6 - Prob. 42ESCh. R.6 - Prob. 43ESCh. R.6 - Prob. 44ESCh. R.6 - Prob. 45ESCh. R.6 - Prob. 46ESCh. R.6 - Prob. 47ESCh. R.6 - Prob. 48ESCh. R.6 - Prob. 49ESCh. R.6 - Prob. 50ESCh. R.6 - Prob. 51ESCh. R.6 - Prob. 52ESCh. R.6 - Prob. 53ESCh. R.6 - Prob. 54ESCh. R.6 - Prob. 55ESCh. R.6 - Prob. 56ES
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- 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.arrow_forward(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_forward
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