 2.1: Treating year as the independent variable and the winning value as ...
 2.2: Interpret the slopes in your equations from part 1. Do the yinterc...
 2.3: Use your equations to predict the winning time in the 2004 Olympics...
 2.4: Repeat parts 1 to 3 using the data for the years 1996 and 2000. How...
 2.5: Would your equations be useful in predicting the winning marathon t...
 2.6: Pick your favorite Winter Olympics event and find the winning value...
 2.7: In 18, find the real solution(s) of each equation.x  2 = 1
 2.8: In 18, find the real solution(s) of each equation.+ 4x = 2
 2.9: In 9 and 10, solve each equation in the complex number system.2 = 9
 2.10: In 9 and 10, solve each equation in the complex number system.2 x ...
 2.11: In 1114, solve each inequality. Graph the solution set.2x  3 7
 2.12: In 1114, solve each inequality. Graph the solution set.1 6 x + 4 6 5
 2.13: In 1114, solve each inequality. Graph the solution set.x  2 1
 2.14: In 1114, solve each inequality. Graph the solution set.2 + x 7 3
 2.15: Find the distance between the points and .Find the midpoint of the ...
 2.16: Which of the following points are on the graph of y = x3  3x + 1?(...
 2.17: Sketch the graph ofy = x3
 2.18: Find the equation of the line containing the points and . Express y...
 2.19: Find the equation of the line perpendicular to the line and contain...
 2.20: Graph the equation x . 2 + y2  4x + 8y  5 = 0
 2.21: In 2126, find the center and radius of each circle. Graph each circ...
 2.22: In 2126, find the center and radius of each circle. Graph each circ...
 2.23: In 2126, find the center and radius of each circle. Graph each circ...
 2.24: In 2126, find the center and radius of each circle. Graph each circ...
 2.25: In 2126, find the center and radius of each circle. Graph each circ...
 2.26: In 2126, find the center and radius of each circle. Graph each circ...
 2.27: In 2736, find an equation of the line having the given characterist...
 2.28: In 2736, find an equation of the line having the given characterist...
 2.29: In 2736, find an equation of the line having the given characterist...
 2.30: In 2736, find an equation of the line having the given characterist...
 2.31: In 2736, find an equation of the line having the given characterist...
 2.32: In 2736, find an equation of the line having the given characterist...
 2.33: In 2736, find an equation of the line having the given characterist...
 2.34: In 2736, find an equation of the line having the given characterist...
 2.35: In 2736, find an equation of the line having the given characterist...
 2.36: In 2736, find an equation of the line having the given characterist...
 2.37: In 3740, find the slope and yintercept of each line. Graph the lin...
 2.38: In 3740, find the slope and yintercept of each line. Graph the lin...
 2.39: In 3740, find the slope and yintercept of each line. Graph the lin...
 2.40: In 3740, find the slope and yintercept of each line. Graph the lin...
 2.41: In 4144, find the intercepts and graph each line. 2x  3y = 12
 2.42: In 4144, find the intercepts and graph each line. x  2y = 8
 2.43: In 4144, find the intercepts and graph each line. 12x +13y = 2
 2.44: In 4144, find the intercepts and graph each line. 13x  14y = 1
 2.45: Sketch a graph of .y = x3
 2.46: Sketch a graph of .y = 2x
 2.47: Graph the line with slope containing the point2 3
 2.48: Show that the points , andare the vertices of an isosceles triangle...
 2.49: Show that the points , and are the vertices of a right triangle in ...
 2.50: The endpoints of the diameter of a circle are and . Find the center...
 2.51: Show that the points , and lie on a line by using slopes.A = 12, 52...
 2.52: Mortgage Payments The monthly payment p on a mortgage varies direct...
 2.53: Revenue Function At the corner Esso station, the revenue R varies d...
 2.54: Weight of a Body The weight of a body variesinversely with the squa...
 2.55: Keplers Third Law of Planetary Motion Keplers Third Law of Planetar...
 2.56: Create four problems that you might be asked to do given the two po...
 2.57: Describe each of the following graphs in the plane. Give justifica...
 2.58: Suppose that you have a rectangular field that requires watering. Y...
Solutions for Chapter 2: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 2
Get Full SolutionsChapter 2 includes 58 full stepbystep solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. Since 58 problems in chapter 2 have been answered, more than 55688 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. This expansive textbook survival guide covers the following chapters and their solutions.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Outer product uv T
= column times row = rank one matrix.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).