 Chapter 1: QUADRATIC EQUATIONS
 Chapter 10: PERIODIC BEHAVIOUR
 Chapter 11: TRIGONOMETRIC EQUATIONS
 Chapter 12: VECTORS AND SCALARS
 Chapter 13: PROBLEMS INVOLVING VECTOR OPERATIONS
 Chapter 14: LIMITS
 Chapter 15: Rules of differentiation
 Chapter 16: Properties of curves
 Chapter 17: Applications of differential calculus
 Chapter 18: Integration
 Chapter 19: Applications of integration
 Chapter 2: RELATIONS AND FUNCTIONS
 Chapter 20: Descriptive statistics
 Chapter 21: Linear modelling
 Chapter 22: Probability
 Chapter 23: Discrete random variables
 Chapter 24: The normal distribution
 Chapter 25: Miscellaneous questions
 Chapter 3: EXPONENTS
 Chapter 4: LOGARITHMS IN BASE 10
 Chapter 5: GRAPHING FUNCTIONS
 Chapter 6: NUMBER SEQUENCES
 Chapter 7: BINOMIAL EXPANSIONS
 Chapter 8: RADIAN MEASURE
 Chapter 9: AREAS OF TRIANGLES
Mathematics for the International Student: Mathematics SL 3rd Edition  Solutions by Chapter
Full solutions for Mathematics for the International Student: Mathematics SL  3rd Edition
ISBN: 9781921972089
Mathematics for the International Student: Mathematics SL  3rd Edition  Solutions by Chapter
Get Full SolutionsSince problems from 25 chapters in Mathematics for the International Student: Mathematics SL have been answered, more than 3103 students have viewed full stepbystep answer. This textbook survival guide was created for the textbook: Mathematics for the International Student: Mathematics SL, edition: 3. Mathematics for the International Student: Mathematics SL was written by and is associated to the ISBN: 9781921972089. The full stepbystep solution to problem in Mathematics for the International Student: Mathematics SL were answered by , our top Math solution expert on 03/15/18, 06:04PM. This expansive textbook survival guide covers the following chapters: 25.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Column space C (A) =
space of all combinations of the columns of A.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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 matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

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.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

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.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

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.

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.

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

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

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

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