 Appendix C.1: Decide whether each relation defines a function. See Example 1. 1. ...
 Appendix C.2: Decide whether each relation defines a function. See Example 1. 2. ...
 Appendix C.3: Decide whether each relation defines a function. See Example 1. 3. ...
 Appendix C.4: Decide whether each relation defines a function. See Example 1. 4. ...
 Appendix C.5: Decide whether each relation defines a function. See Example 1. 5. ...
 Appendix C.6: Decide whether each relation defines a function. See Example 1. 6. ...
 Appendix C.7: Decide whether each relation defines a function. See Example 1. 7. ...
 Appendix C.8: Decide whether each relation defines a function. See Example 1. 8. ...
 Appendix C.9: Decide whether each relation defines a function and give the domain...
 Appendix C.10: Decide whether each relation defines a function and give the domain...
 Appendix C.11: Decide whether each relation defines a function and give the domain...
 Appendix C.12: Decide whether each relation defines a function and give the domain...
 Appendix C.13: Decide whether each relation defines a function and give the domain...
 Appendix C.14: Decide whether each relation defines a function and give the domain...
 Appendix C.15: Decide whether each relation defines a function and give the domain...
 Appendix C.16: Decide whether each relation defines a function and give the domain...
 Appendix C.17: Decide whether each relation defines a function and give the domain...
 Appendix C.18: Decide whether each relation defines a function and give the domain...
 Appendix C.19: Decide whether each relation defines a function and give the domain...
 Appendix C.20: Decide whether each relation defines a function and give the domain...
 Appendix C.21: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.22: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.23: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.24: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.25: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.26: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.27: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.28: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.29: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.30: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.31: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.32: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.33: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.34: Decide whether each relation defines y as a function of x. Give the...
 Appendix C.35: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.36: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.37: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.38: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.39: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.40: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.41: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.42: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.43: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.44: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.45: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.46: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.47: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.48: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.49: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.50: Let 1x2 = 3x + 4 and g1x2 = x2 + 4x + 1. Find and simplify each o...
 Appendix C.51: For each function, find (a) 122 and (b) 112. See Example 7. = 511...
 Appendix C.52: For each function, find (a) 122 and (b) 112. See Example 7. = 512,...
 Appendix C.53: For each function, find (a) 122 and (b) 112. See Example 7. 1 2 3 ...
 Appendix C.54: For each function, find (a) 122 and (b) 112. See Example 7. 2 5 1 ...
 Appendix C.55: For each function, find (a) 122 and (b) 112. See Example 7.
 Appendix C.56: For each function, find (a) 122 and (b) 112. See Example 7.
 Appendix C.57: In Exercises 5760, use the graph of y = 1x2 to find each function v...
 Appendix C.58: In Exercises 5760, use the graph of y = 1x2 to find each function v...
 Appendix C.59: In Exercises 5760, use the graph of y = 1x2 to find each function v...
 Appendix C.60: In Exercises 5760, use the graph of y = 1x2 to find each function v...
 Appendix C.61: Determine the intervals of the domain for which each function is (a...
 Appendix C.62: Determine the intervals of the domain for which each function is (a...
 Appendix C.63: Determine the intervals of the domain for which each function is (a...
 Appendix C.64: Determine the intervals of the domain for which each function is (a...
 Appendix C.65: Determine the intervals of the domain for which each function is (a...
 Appendix C.66: Determine the intervals of the domain for which each function is (a...
Solutions for Chapter Appendix C: Appendix C Exercises
Full solutions for Trigonometry  10th Edition
ISBN: 9780321671776
Solutions for Chapter Appendix C: Appendix C Exercises
Get Full SolutionsChapter Appendix C: Appendix C Exercises includes 66 full stepbystep solutions. Trigonometry was written by and is associated to the ISBN: 9780321671776. This textbook survival guide was created for the textbook: Trigonometry, edition: 10. This expansive textbook survival guide covers the following chapters and their solutions. Since 66 problems in chapter Appendix C: Appendix C Exercises have been answered, more than 34014 students have viewed full stepbystep solutions from this chapter.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

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

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

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.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

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).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

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.

Solvable system Ax = b.
The right side b is in the column space of A.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

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

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.