 2.1.1: Is it possible for a point plotted in the Cartesian coordinate syst...
 2.1.2: Describe the process for finding the xintercept and the yintercep...
 2.1.3: Describe in your own words what the yintercept of a graph is.
 2.1.4: When using the distance formula d = (x2 x1 )2 + (y2 y1 )2 , explain...
 2.1.5: For each of the following exercises, find the xintercept and the y...
 2.1.6: For each of the following exercises, find the xintercept and the y...
 2.1.7: For each of the following exercises, find the xintercept and the y...
 2.1.8: For each of the following exercises, find the xintercept and the y...
 2.1.9: For each of the following exercises, find the xintercept and the y...
 2.1.10: For each of the following exercises, find the xintercept and the y...
 2.1.11: For each of the following exercises, solve the equation for y in te...
 2.1.12: For each of the following exercises, solve the equation for y in te...
 2.1.13: For each of the following exercises, solve the equation for y in te...
 2.1.14: For each of the following exercises, solve the equation for y in te...
 2.1.15: For each of the following exercises, solve the equation for y in te...
 2.1.16: For each of the following exercises, solve the equation for y in te...
 2.1.17: For each of the following exercises, find the distance between the ...
 2.1.18: For each of the following exercises, find the distance between the ...
 2.1.19: For each of the following exercises, find the distance between the ...
 2.1.20: For each of the following exercises, find the distance between the ...
 2.1.21: Find the distance between the two points given using your calculato...
 2.1.22: For each of the following exercises, find the coordinates of the mi...
 2.1.23: For each of the following exercises, find the coordinates of the mi...
 2.1.24: For each of the following exercises, find the coordinates of the mi...
 2.1.25: For each of the following exercises, find the coordinates of the mi...
 2.1.26: For each of the following exercises, find the coordinates of the mi...
 2.1.27: For each of the following exercises, identify the information reque...
 2.1.28: For each of the following exercises, identify the information reque...
 2.1.29: For each of the following exercises, identify the information reque...
 2.1.30: For each of the following exercises, plot the three points on the g...
 2.1.31: For each of the following exercises, plot the three points on the g...
 2.1.32: For each of the following exercises, plot the three points on the g...
 2.1.33: For each of the following exercises, plot the three points on the g...
 2.1.34: Name the quadrant in which the following points would be located. I...
 2.1.35: For each of the following exercises, construct a table and graph th...
 2.1.36: For each of the following exercises, construct a table and graph th...
 2.1.37: For each of the following exercises, construct a table and graph th...
 2.1.38: For each of the following exercises, find and plot the x and yint...
 2.1.39: For each of the following exercises, find and plot the x and yint...
 2.1.40: For each of the following exercises, find and plot the x and yint...
 2.1.41: For each of the following exercises, find and plot the x and yint...
 2.1.42: For each of the following exercises, find and plot the x and yint...
 2.1.43: For each of the following exercises, use the graph in the figure be...
 2.1.44: For each of the following exercises, use the graph in the figure be...
 2.1.45: For each of the following exercises, use the graph in the figure be...
 2.1.46: For each of the following exercises, use the graph in the figure be...
 2.1.47: For each of the following exercises, use the graph in the figure be...
 2.1.48: For the following exercises, use your graphing calculator to input ...
 2.1.49: For the following exercises, use your graphing calculator to input ...
 2.1.50: For the following exercises, use your graphing calculator to input ...
 2.1.51: For the following exercises, use your graphing calculator to input ...
 2.1.52: For the following exercises, use your graphing calculator to input ...
 2.1.53: For the following exercises, use your graphing calculator to input ...
 2.1.54: A man drove 10 mi directly east from his home, made a left turn at ...
 2.1.55: If the road was made in the previous exercise, how much shorter wou...
 2.1.56: Given these four points: A(1, 3), B(3, 5), C(4, 7), and D(5, 4), fi...
 2.1.57: After finding the two midpoints in the previous exercise, find the ...
 2.1.58: Given the graph of the rectangle shown and the coordinates of its v...
 2.1.59: In the previous exercise, find the coordinates of the midpoint for ...
 2.1.60: The coordinates on a map for San Francisco are (53, 17) and those f...
 2.1.61: If San Joses coordinates are (76, 12), where the coordinates repres...
 2.1.62: A small craft in Lake Ontario sends out a distress signal. The coor...
 2.1.63: A man on the top of a building wants to have a guy wire extend to a...
 2.1.64: If we rent a truck and pay a $75/day fee plus $.20 for every mile w...
Solutions for Chapter 2.1: THE RECTANGULAR COORDINATE SYSTEMS AND GRAPHS
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 2.1: THE RECTANGULAR COORDINATE SYSTEMS AND GRAPHS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra, edition: 1. Since 64 problems in chapter 2.1: THE RECTANGULAR COORDINATE SYSTEMS AND GRAPHS have been answered, more than 24833 students have viewed full stepbystep solutions from this chapter. Chapter 2.1: THE RECTANGULAR COORDINATE SYSTEMS AND GRAPHS includes 64 full stepbystep solutions. College Algebra was written by and is associated to the ISBN: 9781938168383.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).