 6.2.1: In Exercises 124, use Gaussian elimination to find the complete so...
 6.2.2: In Exercises 124, use Gaussian elimination to find the complete so...
 6.2.3: In Exercises 124, use Gaussian elimination to find the complete so...
 6.2.4: In Exercises 124, use Gaussian elimination to find the complete so...
 6.2.5: In Exercises 124, use Gaussian elimination to find the complete so...
 6.2.6: In Exercises 124, use Gaussian elimination to find the complete so...
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 6.2.8: In Exercises 124, use Gaussian elimination to find the complete so...
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 6.2.12: In Exercises 124, use Gaussian elimination to find the complete so...
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 6.2.21: In Exercises 124, use Gaussian elimination to find the complete so...
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 6.2.23: In Exercises 124, use Gaussian elimination to find the complete so...
 6.2.24: In Exercises 124, use Gaussian elimination to find the complete so...
 6.2.25: In Exercises 2528. the first screen shows the augmented matrix, A ...
 6.2.26: In Exercises 2528. the first screen shows the augmented matrix, A ...
 6.2.27: In Exercises 2528. the first screen shows the augmented matrix, A ...
 6.2.28: In Exercises 2528. the first screen shows the augmented matrix, A ...
 6.2.29: The figure for Exercises 2932 shows the illlersections of three on...
 6.2.30: The figure for Exercises 2932 shows the illlersections of three on...
 6.2.31: The figure for Exercises 2932 shows the illlersections of three on...
 6.2.32: The figure for Exercises 2932 shows the illlersections of three on...
 6.2.33: The figure shows the intersections of four oneway streets. 100 Car...
 6.2.34: The vitamin content per ounce for lhree foods is given in the follo...
 6.2.35: Three foods have the following nutlitional conte nt pe r ounce. Uni...
 6.2.36: A company thai manufactures products A, B, and C doc< both manufact...
 6.2.37: Describe what happens when Gaussian elimination is used to solve an...
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 6.2.39: In solving a system of dependent equations in three variables. one ...
 6.2.40: a. The figure shows the intersections of a numbc1 of oneway slrcct...
 6.2.41: In Exercises 4144, determine whether each statement makes sense or...
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 6.2.44: In Exercises 4144, determine whether each statement makes sense or...
 6.2.45: Consider the linea r system { x + 3v + : a' 2r  5y T 2a:  0 x  y...
 6.2.46: Before beginning this exercise. the group needs to read and solve E...
 6.2.47: Exercises 4749 will help )'Oll prepare for the lllllterial covered...
 6.2.48: Exercises 4749 will help )'Oll prepare for the lllllterial covered...
 6.2.49: Exercises 4749 will help )'Oll prepare for the lllllterial covered...
Solutions for Chapter 6.2: Inconsistent and Dependent Systems and Their Applications
Full solutions for College Algebra  6th Edition
ISBN: 9780321782281
Solutions for Chapter 6.2: Inconsistent and Dependent Systems and Their Applications
Get Full SolutionsChapter 6.2: Inconsistent and Dependent Systems and Their Applications includes 49 full stepbystep solutions. College Algebra was written by and is associated to the ISBN: 9780321782281. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 6. Since 49 problems in chapter 6.2: Inconsistent and Dependent Systems and Their Applications have been answered, more than 38879 students have viewed full stepbystep solutions from this chapter.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

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

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

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

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

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

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.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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

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.

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·

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