 6.2.31: In Exercises 3134, match the system of linear equations withits gra...
 6.2.32: In Exercises 3134, match the system of linear equations withits gra...
 6.2.33: In Exercises 3134, match the system of linear equations withits gra...
 6.2.34: In Exercises 3134, match the system of linear equations withits gra...
 6.2.35: In Exercises 3542, use any method to solve the system. 3x 5y 72x y 9
 6.2.36: In Exercises 3542, use any method to solve the system. x 3y 174x 3y 7
 6.2.37: In Exercises 3542, use any method to solve the system. y 2x 5y 5x 11
 6.2.38: In Exercises 3542, use any method to solve the system.7x 3y 16y x 2
 6.2.39: In Exercises 3542, use any method to solve the system. x 5y 216x 5y 21
 6.2.40: In Exercises 3542, use any method to solve the system. y 2x 17y 2 3x
 6.2.41: In Exercises 3542, use any method to solve the system. 5x 9y 13y x 4
 6.2.42: In Exercises 3542, use any method to solve the system. 4x 3y 65x 7y 1
 6.2.43: AIRPLANE SPEED An airplane flying into aheadwind travels the 1800m...
 6.2.44: AIRPLANE SPEED Two planes start from LosAngeles International Airpo...
 6.2.45: SUPPLY AND DEMAND In Exercises 4548, find theequilibrium point of t...
 6.2.46: SUPPLY AND DEMAND In Exercises 4548, find theequilibrium point of t...
 6.2.47: SUPPLY AND DEMAND In Exercises 4548, find theequilibrium point of t...
 6.2.48: SUPPLY AND DEMAND In Exercises 4548, find theequilibrium point of t...
 6.2.49: NUTRITION Two cheeseburgers and one small orderof French fries from...
 6.2.50: NUTRITION One eightounce glass of apple juice andone eightounce g...
 6.2.51: ACID MIXTURE Thirty liters of a 40% acid solution isobtained by mix...
 6.2.52: FUEL MIXTURE Five hundred gallons of 89octanegasoline is obtained ...
 6.2.53: INVESTMENT PORTFOLIO A total of $24,000 isinvested in two corporate...
 6.2.54: INVESTMENT PORTFOLIO A total of $32,000 isinvested in two municipal...
 6.2.55: PRESCRIPTIONS The numbers of prescriptions (inthousands) filled at ...
 6.2.56: DATA ANALYSIS A store manager wants to know thedemand for a product...
 6.2.57: FITTING A LINE TO DATA In Exercises 5760, find theleast squares reg...
 6.2.58: FITTING A LINE TO DATA In Exercises 5760, find theleast squares reg...
 6.2.59: FITTING A LINE TO DATA In Exercises 5760, find theleast squares reg...
 6.2.60: FITTING A LINE TO DATA In Exercises 5760, find theleast squares reg...
 6.2.61: DATA ANALYSIS An agricultural scientist used fourtest plots to dete...
 6.2.62: DEFENSE DEPARTMENT OUTLAYS The table showsthe total national outlay...
 6.2.63: TRUE OR FALSE? In Exercises 63 and 64, determinewhether the stateme...
 6.2.64: TRUE OR FALSE? In Exercises 63 and 64, determinewhether the stateme...
 6.2.65: WRITING Briefly explain whether or not it is possiblefor a consiste...
 6.2.66: THINK ABOUT IT Give examples of a system of linearequations that ha...
 6.2.67: COMPARING METHODS Use the method of substitutionto solve the system...
 6.2.68: CAPSTONE Rewrite each system of equations inslopeintercept form an...
 6.2.69: THINK ABOUT IT In Exercises 69 and 70, the graphs of thetwo equatio...
 6.2.70: THINK ABOUT IT In Exercises 69 and 70, the graphs of thetwo equatio...
 6.2.71: In Exercises 71 and 72, find the value of such that thesystem of li...
 6.2.72: In Exercises 71 and 72, find the value of such that thesystem of li...
Solutions for Chapter 6.2: TwoVariable Linear Systems
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter 6.2: TwoVariable Linear Systems
Get Full SolutionsSince 42 problems in chapter 6.2: TwoVariable Linear Systems have been answered, more than 33218 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra , edition: 8. College Algebra was written by and is associated to the ISBN: 9781439048696. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 6.2: TwoVariable Linear Systems includes 42 full stepbystep solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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

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.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

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

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

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

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.