Intermediate Algebra
10th Edition
ISBN: 9781285195728
Author: Jerome E. Kaufmann, Karen L. Schwitters
Publisher: Cengage Learning
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Chapter 7.3, Problem 20PS
To determine
To find:
The graph of line determined by the two given points and the slope of the line.
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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 7 Solutions
Intermediate Algebra
Ch. 7.1 - For Problems 1-10, answer true or false. In a...Ch. 7.1 - For Problems 110, answer true or false. Quadrants...Ch. 7.1 - For Problems 110, answer true or false. The real...Ch. 7.1 - Prob. 4CQCh. 7.1 - Prob. 5CQCh. 7.1 - For Problems 1-10, answer true or false. Graph of...Ch. 7.1 - Prob. 7CQCh. 7.1 - Prob. 8CQCh. 7.1 - Prob. 9CQCh. 7.1 - Prob. 10CQ
Ch. 7.1 - Prob. 1PSCh. 7.1 - Prob. 2PSCh. 7.1 - Prob. 3PSCh. 7.1 - Prob. 4PSCh. 7.1 - Prob. 5PSCh. 7.1 - Prob. 6PSCh. 7.1 - Prob. 7PSCh. 7.1 - Prob. 8PSCh. 7.1 - Prob. 9PSCh. 7.1 - Prob. 10PSCh. 7.1 - For Problems 928, graph each of the linear...Ch. 7.1 - Prob. 12PSCh. 7.1 - Prob. 13PSCh. 7.1 - Prob. 14PSCh. 7.1 - Prob. 15PSCh. 7.1 - Prob. 16PSCh. 7.1 - Prob. 17PSCh. 7.1 - Prob. 18PSCh. 7.1 - Prob. 19PSCh. 7.1 - Prob. 20PSCh. 7.1 - Prob. 21PSCh. 7.1 - Prob. 22PSCh. 7.1 - Prob. 23PSCh. 7.1 - Prob. 24PSCh. 7.1 - Prob. 25PSCh. 7.1 - Prob. 26PSCh. 7.1 - Prob. 27PSCh. 7.1 - Prob. 28PSCh. 7.1 - Prob. 29PSCh. 7.1 - Prob. 30PSCh. 7.1 - Prob. 31PSCh. 7.1 - Prob. 32PSCh. 7.1 - Prob. 33PSCh. 7.1 - Prob. 34PSCh. 7.1 - Prob. 35PSCh. 7.1 - Prob. 36PSCh. 7.1 - Prob. 37PSCh. 7.1 - Prob. 38PSCh. 7.1 - Prob. 39PSCh. 7.1 - Prob. 40PSCh. 7.1 - Prob. 41PSCh. 7.1 - Prob. 42PSCh. 7.1 - Prob. 43PSCh. 7.1 - Prob. 44PSCh. 7.1 - Prob. 45PSCh. 7.1 - Prob. 46PSCh. 7.1 - Prob. 47PSCh. 7.1 - Prob. 48PSCh. 7.1 - Prob. 49PSCh. 7.1 - Prob. 50PSCh. 7.1 - Prob. 51PSCh. 7.1 - Prob. 52PSCh. 7.1 - Prob. 53PSCh. 7.1 - Prob. 54PSCh. 7.1 - Prob. 55PSCh. 7.1 - Prob. 56PSCh. 7.1 - Prob. 57PSCh. 7.1 - Prob. 58PSCh. 7.1 - Now lets use a graphing calculator to get a graph...Ch. 7.1 - Prob. 60PSCh. 7.2 - Prob. 1CQCh. 7.2 - Prob. 2CQCh. 7.2 - Prob. 3CQCh. 7.2 - Prob. 4CQCh. 7.2 - Prob. 5CQCh. 7.2 - Prob. 6CQCh. 7.2 - Prob. 7CQCh. 7.2 - Prob. 8CQCh. 7.2 - Prob. 9CQCh. 7.2 - Prob. 10CQCh. 7.2 - Prob. 1PSCh. 7.2 - Prob. 2PSCh. 7.2 - Prob. 3PSCh. 7.2 - Prob. 4PSCh. 7.2 - Prob. 5PSCh. 7.2 - Prob. 6PSCh. 7.2 - Prob. 7PSCh. 7.2 - Prob. 8PSCh. 7.2 - Prob. 9PSCh. 7.2 - Prob. 10PSCh. 7.2 - Prob. 11PSCh. 7.2 - Prob. 12PSCh. 7.2 - Prob. 13PSCh. 7.2 - Prob. 14PSCh. 7.2 - Prob. 15PSCh. 7.2 - Prob. 16PSCh. 7.2 - Prob. 17PSCh. 7.2 - Prob. 18PSCh. 7.2 - Prob. 19PSCh. 7.2 - Prob. 20PSCh. 7.2 - Prob. 21PSCh. 7.2 - Prob. 22PSCh. 7.2 - Prob. 23PSCh. 7.2 - Prob. 24PSCh. 7.2 - Prob. 25PSCh. 7.2 - For Problems 130, graph each of the inequalities....Ch. 7.2 - Prob. 27PSCh. 7.2 - Prob. 28PSCh. 7.2 - Prob. 29PSCh. 7.2 - Prob. 30PSCh. 7.2 - Prob. 31PSCh. 7.2 - Prob. 32PSCh. 7.2 - Prob. 33PSCh. 7.2 - Prob. 34PSCh. 7.2 - Prob. 35PSCh. 7.2 - Prob. 36PSCh. 7.2 - Prob. 37.1PSCh. 7.2 - Prob. 37.2PSCh. 7.2 - Prob. 37.3PSCh. 7.2 - Prob. 38PSCh. 7.2 - Prob. 39.1PSCh. 7.2 - Prob. 39.2PSCh. 7.2 - Prob. 39.3PSCh. 7.2 - Prob. 39.4PSCh. 7.3 - For Problems 110, answer true or false. hen...Ch. 7.3 - Prob. 2CQCh. 7.3 - Prob. 3CQCh. 7.3 - Prob. 4CQCh. 7.3 - Prob. 5CQCh. 7.3 - Prob. 6CQCh. 7.3 - Prob. 7CQCh. 7.3 - Prob. 8CQCh. 7.3 - Prob. 9CQCh. 7.3 - Prob. 10CQCh. 7.3 - Prob. 1PSCh. 7.3 - Prob. 2PSCh. 7.3 - Prob. 3PSCh. 7.3 - Prob. 4PSCh. 7.3 - Prob. 5PSCh. 7.3 - Prob. 6PSCh. 7.3 - Prob. 7PSCh. 7.3 - Prob. 8PSCh. 7.3 - Prob. 9PSCh. 7.3 - Prob. 10PSCh. 7.3 - Prob. 11PSCh. 7.3 - Prob. 12PSCh. 7.3 - Prob. 13PSCh. 7.3 - Prob. 14PSCh. 7.3 - Prob. 15PSCh. 7.3 - Prob. 16PSCh. 7.3 - Prob. 17PSCh. 7.3 - Prob. 18PSCh. 7.3 - Prob. 19PSCh. 7.3 - Prob. 20PSCh. 7.3 - Prob. 21PSCh. 7.3 - Prob. 22PSCh. 7.3 - Prob. 23PSCh. 7.3 - Prob. 24PSCh. 7.3 - Prob. 25PSCh. 7.3 - Prob. 26PSCh. 7.3 - Prob. 27PSCh. 7.3 - Prob. 28PSCh. 7.3 - Prob. 29PSCh. 7.3 - Prob. 30PSCh. 7.3 - Prob. 31PSCh. 7.3 - Prob. 32PSCh. 7.3 - Prob. 33PSCh. 7.3 - Prob. 34PSCh. 7.3 - Prob. 35PSCh. 7.3 - Prob. 36PSCh. 7.3 - For Problems 33-40, you are given one point on a...Ch. 7.3 - Prob. 38PSCh. 7.3 - Prob. 39PSCh. 7.3 - Prob. 40PSCh. 7.3 - Prob. 41PSCh. 7.3 - Prob. 42PSCh. 7.3 - Prob. 43PSCh. 7.3 - Prob. 44PSCh. 7.3 - Prob. 45PSCh. 7.3 - Prob. 46PSCh. 7.3 - Prob. 47PSCh. 7.3 - Prob. 48PSCh. 7.3 - Prob. 49PSCh. 7.3 - Prob. 50PSCh. 7.3 - Prob. 51PSCh. 7.3 - Prob. 52PSCh. 7.3 - Prob. 53PSCh. 7.3 - Prob. 54PSCh. 7.3 - Prob. 55PSCh. 7.3 - Prob. 56PSCh. 7.3 - Prob. 57PSCh. 7.3 - Prob. 58PSCh. 7.3 - Prob. 59PSCh. 7.3 - Prob. 60PSCh. 7.3 - Prob. 61PSCh. 7.3 - Prob. 62PSCh. 7.3 - Prob. 63PSCh. 7.3 - Prob. 64PSCh. 7.3 - Prob. 65PSCh. 7.3 - If one line has a slope of 25, and another line...Ch. 7.3 - Prob. 67PSCh. 7.3 - Prob. 68PSCh. 7.3 - Prob. 69PSCh. 7.3 - Prob. 70PSCh. 7.3 - Prob. 71PSCh. 7.3 - Prob. 72PSCh. 7.4 - Prob. 1CQCh. 7.4 - Prob. 2CQCh. 7.4 - Prob. 3CQCh. 7.4 - Prob. 4CQCh. 7.4 - For Problems 110, answer true or false. In the...Ch. 7.4 - Prob. 6CQCh. 7.4 - Prob. 7CQCh. 7.4 - Prob. 8CQCh. 7.4 - Prob. 9CQCh. 7.4 - Prob. 10CQCh. 7.4 - Prob. 1PSCh. 7.4 - Prob. 2PSCh. 7.4 - Prob. 3PSCh. 7.4 - Prob. 4PSCh. 7.4 - Prob. 5PSCh. 7.4 - Prob. 6PSCh. 7.4 - Prob. 7PSCh. 7.4 - Prob. 8PSCh. 7.4 - Prob. 9PSCh. 7.4 - Prob. 10PSCh. 7.4 - Prob. 11PSCh. 7.4 - Prob. 12PSCh. 7.4 - Prob. 13PSCh. 7.4 - Prob. 14PSCh. 7.4 - Prob. 15PSCh. 7.4 - Prob. 16PSCh. 7.4 - Prob. 17PSCh. 7.4 - Prob. 18PSCh. 7.4 - Prob. 19PSCh. 7.4 - Prob. 20PSCh. 7.4 - Prob. 21PSCh. 7.4 - Prob. 22PSCh. 7.4 - Prob. 23PSCh. 7.4 - Prob. 24PSCh. 7.4 - Prob. 25PSCh. 7.4 - Prob. 26PSCh. 7.4 - Prob. 27PSCh. 7.4 - Prob. 28PSCh. 7.4 - Prob. 29PSCh. 7.4 - Prob. 30PSCh. 7.4 - For Problems 2532, write the equation of the line...Ch. 7.4 - Prob. 32PSCh. 7.4 - Prob. 33PSCh. 7.4 - Prob. 34PSCh. 7.4 - Prob. 35PSCh. 7.4 - Prob. 36PSCh. 7.4 - Prob. 37PSCh. 7.4 - Prob. 38PSCh. 7.4 - Prob. 39PSCh. 7.4 - Prob. 40PSCh. 7.4 - Prob. 41PSCh. 7.4 - Prob. 42PSCh. 7.4 - Prob. 43PSCh. 7.4 - Prob. 44PSCh. 7.4 - Prob. 45PSCh. 7.4 - Prob. 46PSCh. 7.4 - Prob. 47PSCh. 7.4 - Prob. 48PSCh. 7.4 - Prob. 49PSCh. 7.4 - Prob. 50PSCh. 7.4 - Prob. 51PSCh. 7.4 - For Problems 4954, change the equation to...Ch. 7.4 - Prob. 53PSCh. 7.4 - Prob. 54PSCh. 7.4 - Prob. 55PSCh. 7.4 - Prob. 56PSCh. 7.4 - Prob. 57PSCh. 7.4 - Prob. 58PSCh. 7.4 - Prob. 59PSCh. 7.4 - Prob. 60PSCh. 7.4 - Prob. 61PSCh. 7.4 - Prob. 62PSCh. 7.4 - Prob. 63PSCh. 7.4 - Prob. 64PSCh. 7.4 - Prob. 65PSCh. 7.4 - Prob. 66PSCh. 7.4 - Prob. 67PSCh. 7.4 - Prob. 68PSCh. 7.4 - Prob. 69PSCh. 7.4 - Prob. 70PSCh. 7.4 - Prob. 71PSCh. 7.4 - Prob. 72PSCh. 7.4 - Prob. 73PSCh. 7.4 - Prob. 74PSCh. 7.4 - Prob. 75PSCh. 7.4 - Prob. 76PSCh. 7.4 - Prob. 77PSCh. 7.4 - Prob. 78PSCh. 7.4 - Prob. 79PSCh. 7.4 - Prob. 80PSCh. 7.4 - Prob. 81PSCh. 7.4 - Prob. 82PSCh. 7.4 - Prob. 83PSCh. 7.4 - The properties in Problem 83 provide us with...Ch. 7.4 - Prob. 85PSCh. 7.4 - Prob. 86PSCh. 7.5 - Prob. 1CQCh. 7.5 - For Problems 110, answer true or false. If a graph...Ch. 7.5 - Prob. 3CQCh. 7.5 - Prob. 4CQCh. 7.5 - Prob. 5CQCh. 7.5 - Prob. 6CQCh. 7.5 - Prob. 7CQCh. 7.5 - Prob. 8CQCh. 7.5 - For Problems 110, answer true or false. The graph...Ch. 7.5 - Prob. 10CQCh. 7.5 - Prob. 1PSCh. 7.5 - Prob. 2PSCh. 7.5 - Prob. 3PSCh. 7.5 - Prob. 4PSCh. 7.5 - Prob. 5PSCh. 7.5 - Prob. 6PSCh. 7.5 - Prob. 7PSCh. 7.5 - Prob. 8PSCh. 7.5 - Prob. 9PSCh. 7.5 - Prob. 10PSCh. 7.5 - Prob. 11PSCh. 7.5 - Prob. 12PSCh. 7.5 - Prob. 13PSCh. 7.5 - Prob. 14PSCh. 7.5 - Prob. 15PSCh. 7.5 - Prob. 16PSCh. 7.5 - Prob. 17PSCh. 7.5 - Prob. 18PSCh. 7.5 - Prob. 19PSCh. 7.5 - Prob. 20PSCh. 7.5 - Prob. 21PSCh. 7.5 - Prob. 22PSCh. 7.5 - Prob. 23PSCh. 7.5 - Prob. 24PSCh. 7.5 - Prob. 25PSCh. 7.5 - Prob. 26PSCh. 7.5 - Prob. 27PSCh. 7.5 - Prob. 28PSCh. 7.5 - Prob. 29PSCh. 7.5 - Prob. 30PSCh. 7.5 - Prob. 31PSCh. 7.5 - Prob. 32PSCh. 7.5 - Prob. 33PSCh. 7.5 - Prob. 34PSCh. 7.5 - Prob. 35PSCh. 7.5 - Prob. 36PSCh. 7.5 - Prob. 37PSCh. 7.5 - Prob. 38PSCh. 7.5 - Prob. 39PSCh. 7.5 - Prob. 40PSCh. 7.5 - Prob. 41PSCh. 7.5 - Prob. 42PSCh. 7.5 - Prob. 43PSCh. 7.5 - Prob. 44PSCh. 7.5 - Prob. 45PSCh. 7.5 - Prob. 46PSCh. 7.5 - Prob. 47PSCh. 7.5 - Prob. 48PSCh. 7.5 - Prob. 49PSCh. 7.5 - Prob. 50PSCh. 7.5 - Prob. 51PSCh. 7.5 - Prob. 52PSCh. 7.5 - Prob. 53PSCh. 7.5 - Prob. 54PSCh. 7.5 - Prob. 55PSCh. 7.5 - Prob. 56PSCh. 7.5 - Prob. 57PSCh. 7.5 - Prob. 58PSCh. 7.5 - Prob. 59PSCh. 7.5 - Prob. 60PSCh. 7.5 - Prob. 61PSCh. 7.5 - Prob. 62PSCh. 7.5 - Is a graph symmetric with respect to both axes if...Ch. 7.5 - Prob. 64PSCh. 7.5 - Prob. 65PSCh. 7.5 - Prob. 66PSCh. 7.5 - Prob. 67PSCh. 7.5 - Prob. 68PSCh. 7.5 - Prob. 69PSCh. 7.S - Prob. 1SCh. 7.S - Prob. 2SCh. 7.S - Prob. 3SCh. 7.S - Prob. 4SCh. 7.S - Prob. 5SCh. 7.S - Prob. 6SCh. 7.S - Prob. 7SCh. 7.S - Prob. 8SCh. 7.S - Prob. 9SCh. 7.S - Prob. 10SCh. 7.S - Prob. 11SCh. 7.S - Prob. 12SCh. 7.S - Prob. 13SCh. 7.S - Prob. 14SCh. 7.S - Prob. 15SCh. 7.S - Prob. 16SCh. 7.CR - Prob. 1CRCh. 7.CR - Prob. 2CRCh. 7.CR - Prob. 3CRCh. 7.CR - Prob. 4CRCh. 7.CR - Prob. 5CRCh. 7.CR - Prob. 6CRCh. 7.CR - Prob. 7CRCh. 7.CR - Prob. 8CRCh. 7.CR - Prob. 9CRCh. 7.CR - Prob. 10CRCh. 7.CR - Prob. 11CRCh. 7.CR - Prob. 12CRCh. 7.CR - Prob. 13CRCh. 7.CR - Prob. 14CRCh. 7.CR - Prob. 15CRCh. 7.CR - Prob. 16CRCh. 7.CR - Prob. 17CRCh. 7.CR - Prob. 18CRCh. 7.CR - Prob. 19CRCh. 7.CR - Prob. 20CRCh. 7.CR - Prob. 21CRCh. 7.CR - Prob. 22CRCh. 7.CR - Prob. 23CRCh. 7.CR - Prob. 24CRCh. 7.CR - Prob. 25CRCh. 7.CR - Prob. 26CRCh. 7.CR - Prob. 27CRCh. 7.CR - Prob. 28CRCh. 7.CR - Prob. 29CRCh. 7.CR - Prob. 30CRCh. 7.CR - Prob. 31CRCh. 7.CR - Prob. 32CRCh. 7.CR - Prob. 33CRCh. 7.CR - Prob. 34CRCh. 7.CR - Prob. 35CRCh. 7.CR - Prob. 36CRCh. 7.CR - Prob. 37CRCh. 7.CR - Prob. 38CRCh. 7.CR - Prob. 39CRCh. 7.CR - Prob. 40CRCh. 7.CR - Prob. 41CRCh. 7.CR - Prob. 42CRCh. 7.CR - Prob. 43CRCh. 7.CR - Prob. 44CRCh. 7.CR - Prob. 45CRCh. 7.CR - Prob. 46CRCh. 7.CR - Prob. 47CRCh. 7.CR - Prob. 48CRCh. 7.CR - Prob. 49CRCh. 7.CR - Prob. 50CRCh. 7.CR - Prob. 51CRCh. 7.CR - Prob. 52CRCh. 7.CR - Prob. 53CRCh. 7.CR - Prob. 54CRCh. 7.CR - Prob. 55CRCh. 7.CR - Prob. 56CRCh. 7.CR - Prob. 57CRCh. 7.CR - Prob. 58CRCh. 7.CR - Prob. 59CRCh. 7.CR - Prob. 60CRCh. 7.CR - Prob. 61CRCh. 7.CR - The taxes for a primary residence can be described...Ch. 7.CR - Prob. 63CRCh. 7.CR - Prob. 64CRCh. 7.CR - The time needed to install computer cables has a...Ch. 7.CR - Determine the types of symmetry symmetry with...Ch. 7.CR - For Problems 6772, graph each equation. y=x3+2Ch. 7.CR - For Problems 6772, graph each equation. y=x3Ch. 7.CR - Prob. 69CRCh. 7.CR - Prob. 70CRCh. 7.CR - Prob. 71CRCh. 7.CR - Prob. 72CRCh. 7.CT - Prob. 1CTCh. 7.CT - Prob. 2CTCh. 7.CT - Prob. 3CTCh. 7.CT - Prob. 4CTCh. 7.CT - Prob. 5CTCh. 7.CT - Prob. 6CTCh. 7.CT - Prob. 7CTCh. 7.CT - Prob. 8CTCh. 7.CT - Prob. 9CTCh. 7.CT - Prob. 10CTCh. 7.CT - Prob. 11CTCh. 7.CT - Prob. 12CTCh. 7.CT - Prob. 13CTCh. 7.CT - Prob. 14CTCh. 7.CT - Prob. 15CTCh. 7.CT - Prob. 16CTCh. 7.CT - Prob. 17CTCh. 7.CT - Prob. 18CTCh. 7.CT - Prob. 19CTCh. 7.CT - Prob. 20CTCh. 7.CT - Prob. 21CTCh. 7.CT - Prob. 22CTCh. 7.CT - For Problems 1823, graph each equation. y=14x14Ch. 7.CT - Prob. 24CTCh. 7.CT - For Problem 24 and 25, graph each inequality....
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