 13.1: Danielle said that there is no integer that makes the inequality 2x...
 13.2: A binomial is a polynomial with two terms and a trinomial is a poly...
 13.3: In 312, write the sum or difference of the given polynomials in sim...
 13.4: In 312, write the sum or difference of the given polynomials in sim...
 13.5: In 312, write the sum or difference of the given polynomials in sim...
 13.6: In 312, write the sum or difference of the given polynomials in sim...
 13.7: In 312, write the sum or difference of the given polynomials in sim...
 13.8: In 312, write the sum or difference of the given polynomials in sim...
 13.9: In 312, write the sum or difference of the given polynomials in sim...
 13.10: In 312, write the sum or difference of the given polynomials in sim...
 13.11: In 312, write the sum or difference of the given polynomials in sim...
 13.12: In 312, write the sum or difference of the given polynomials in sim...
 13.13: In 1322, solve each equation or inequality. Each solution is an int...
 13.14: In 1322, solve each equation or inequality. Each solution is an int...
 13.15: In 1322, solve each equation or inequality. Each solution is an int...
 13.16: In 1322, solve each equation or inequality. Each solution is an int...
 13.17: In 1322, solve each equation or inequality. Each solution is an int...
 13.18: In 1322, solve each equation or inequality. Each solution is an int...
 13.19: In 1322, solve each equation or inequality. Each solution is an int...
 13.20: In 1322, solve each equation or inequality. Each solution is an int...
 13.21: In 1322, solve each equation or inequality. Each solution is an int...
 13.22: In 1322, solve each equation or inequality. Each solution is an int...
 13.23: An online music store is having a sale. Any song costs 75 cents and...
 13.24: The length of a rectangle is 5 feet more than twice the width. a. I...
 13.25: On his trip to work each day, Brady pays the same toll, using eithe...
Solutions for Chapter 13: Adding Polynomials
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 13: Adding Polynomials
Get Full SolutionsSince 25 problems in chapter 13: Adding Polynomials have been answered, more than 28461 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 13: Adding Polynomials includes 25 full stepbystep solutions. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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.

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.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

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.

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.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.