- Chapter 1: An Introduction to Algebra
- Chapter 10: Quadratic Equations, Functions, and Inequalities
- Chapter 11: Exponential and Logarithmic Functions
- Chapter 12: More on Systems of Equations
- Chapter 13: Conic Sections; More Graphing
- Chapter 14: Miscellaneous Topics
- Chapter 2: Equations, Inequalities, and Problem Solving
- Chapter 3: Graphing Linear Equations and Inequalities in Two Variables; Functions
- Chapter 4: Systems of Linear Equations and Inequalities
- Chapter 5: Exponents and Polynomials
- Chapter 6: Factoring and Quadratic Equations
- Chapter 7: Rational Expressions and Equations
- Chapter 8: Transition to Intermediate Algebra
- Chapter 9: Radical Expressions and Equations
Elementary and Intermediate Algebra 5th Edition - Solutions by Chapter
Full solutions for Elementary and Intermediate Algebra | 5th Edition
ISBN: 9781111567682
Solutions by Chapter
Elementary and Intermediate Algebra was written by and is associated to the ISBN: 9781111567682. This textbook survival guide was created for the textbook: Elementary and Intermediate Algebra, edition: 5. The full step-by-step solution to problem in Elementary and Intermediate Algebra were answered by , our top Math solution expert on 01/24/18, 03:12PM. Since problems from 14 chapters in Elementary and Intermediate Algebra have been answered, more than 34054 students have viewed full step-by-step answer. This expansive textbook survival guide covers the following chapters: 14.
Key Math Terms and definitions covered in this textbook
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Cofactor Cij.
Remove row i and column j; multiply the determinant by (-I)i + j •
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Condition number
cond(A) = c(A) = IIAIlIIA-III = 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.
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Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A
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Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.
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Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.
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Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).
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lA-II = 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.
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Length II x II.
Square root of x T x (Pythagoras in n dimensions).
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Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.
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Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.
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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.
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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).
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Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.
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Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.
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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.
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Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!
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Special solutions to As = O.
One free variable is Si = 1, other free variables = o.
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Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.
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Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.
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Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.