 1.3.1: In Exercises 16, (a) determine the polynomial function whose graph ...
 1.3.2: In Exercises 16, (a) determine the polynomial function whose graph ...
 1.3.3: In Exercises 16, (a) determine the polynomial function whose graph ...
 1.3.4: In Exercises 16, (a) determine the polynomial function whose graph ...
 1.3.5: In Exercises 16, (a) determine the polynomial function whose graph ...
 1.3.6: In Exercises 16, (a) determine the polynomial function whose graph ...
 1.3.7: Writing Try to fit the graph of a polynomial function to the values...
 1.3.8: The graph of a function passes through the points and Find a quadra...
 1.3.9: Find a polynomial function of degree 2 or less that passes through ...
 1.3.10: Calculus The graph of a parabola passes through the points and and ...
 1.3.11: Calculus The graph of a cubic polynomial function has horizontal ta...
 1.3.12: Find an equation of the circle passing through the points and
 1.3.13: The U.S. census lists the population of the United States as 227 mi...
 1.3.14: The U.S. population figures for the years 1920, 1930, 1940, and 195...
 1.3.15: The net profits (in millions of dollars) for Microsoft from 2000 to...
 1.3.16: The sales (in billions of dollars) for WalMart stores from 2000 to...
 1.3.17: Use and to estimate .
 1.3.18: Use and to estimate
 1.3.19: Guided Proof Prove that if a polynomial function is zero for and th...
 1.3.20: The statement in Exercise 19 can be generalized: If a polynomial fu...
 1.3.21: Water is flowing through a network of pipes (in thousands of cubic ...
 1.3.22: The flow of traffic (in vehicles per hour) through a network of str...
 1.3.23: The flow of traffic (in vehicles per hour) through a network of str...
 1.3.24: The flow of traffic (in vehicles per hour) through a network of str...
 1.3.25: Determine the currents and for the electrical network shown in Figu...
 1.3.26: Determine the currents and for the electrical network shown in Figu...
 1.3.27: (a) Determine the currents and for the electrical network shown in ...
 1.3.28: Determine the currents and for the electrical network shown in Figu...
 1.3.29: In Exercises 2932, use a system of equations to write the partial f...
 1.3.30: In Exercises 2932, use a system of equations to write the partial f...
 1.3.31: In Exercises 2932, use a system of equations to write the partial f...
 1.3.32: In Exercises 2932, use a system of equations to write the partial f...
 1.3.33: In Exercises 33 and 34, find the values of and that satisfy the sys...
 1.3.34: In Exercises 33 and 34, find the values of and that satisfy the sys...
 1.3.35: In Super Bowl XLI on February 4, 2007, the Indianapolis Colts beat ...
 1.3.36: In the 2007 Fiesta Bowl Championship Series on January 8, 2007, the...
Solutions for Chapter 1.3: Applications of Systems of Linear Equations
Full solutions for Elementary Linear Algebra  6th Edition
ISBN: 9780618783762
Solutions for Chapter 1.3: Applications of Systems of Linear Equations
Get Full SolutionsThis textbook survival guide was created for the textbook: Elementary Linear Algebra, edition: 6. Since 36 problems in chapter 1.3: Applications of Systems of Linear Equations have been answered, more than 18149 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.3: Applications of Systems of Linear Equations includes 36 full stepbystep solutions. Elementary Linear Algebra was written by and is associated to the ISBN: 9780618783762.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

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

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

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

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).

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

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

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

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

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

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

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.