Introduction to Linear Algebra 4th Edition solutions

Introduction to Linear Algebra 4
Problems 1-10 are about elimination on 2 by 2 systems.

Introduction to Linear Algebra 4
Problems 1-10 are about elimination on 2 by 2 systems.

Introduction to Linear Algebra 4
Problems 1-10 are about elimination on 2 by 2 systems.

Introduction to Linear Algebra 4
Problems 1-10 are about elimination on 2 by 2 systems.

Introduction to Linear Algebra 4
Problems 1-10 are about elimination on 2 by 2 systems.

Introduction to Linear Algebra 4
Problems 1-10 are about elimination on 2 by 2 systems.

Introduction to Linear Algebra 4
Problems 1-10 are about elimination on 2 by 2 systems.

Introduction to Linear Algebra 4
Problems 1-10 are about elimination on 2 by 2 systems.

Introduction to Linear Algebra 4
Problems 1-10 are about elimination on 2 by 2 systems.

Introduction to Linear Algebra 4
Problems 1-10 are about elimination on 2 by 2 systems.

Introduction to Linear Algebra 4
Problems 11-20 study elimination on 3 by 3 systems (and possible failure).

Introduction to Linear Algebra 4
Problems 11-20 study elimination on 3 by 3 systems (and possible failure).

Introduction to Linear Algebra 4
Problems 11-20 study elimination on 3 by 3 systems (and possible failure).

Introduction to Linear Algebra 4
Problems 11-20 study elimination on 3 by 3 systems (and possible failure).

Introduction to Linear Algebra 4
Problems 11-20 study elimination on 3 by 3 systems (and possible failure).

Introduction to Linear Algebra 4
Problems 11-20 study elimination on 3 by 3 systems (and possible failure).

Introduction to Linear Algebra 4
Problems 11-20 study elimination on 3 by 3 systems (and possible failure).

Introduction to Linear Algebra 4
Problems 11-20 study elimination on 3 by 3 systems (and possible failure).

Introduction to Linear Algebra 4
Problems 11-20 study elimination on 3 by 3 systems (and possible failure).

Introduction to Linear Algebra 4
Problems 11-20 study elimination on 3 by 3 systems (and possible failure).

Introduction to Linear Algebra 4
Find the pivots and the solution for both systems (Ax = band Kx = b): 2x+ Y =0 2x- y =0 x+2y+ z =0 -x +2y- z =0 y +2z + t=O y +2z- t =0 z +2t = 5 - z + 2t = 5.

Introduction to Linear Algebra 4
If you extend Problem 21 following the 1,2, 1 pattern or the -1,2, -1 pattern, what is the fifth pivot? What is the nth pivot? K is my favorite matrix.

Introduction to Linear Algebra 4
If elimination leads to x + y = 1 and 2y = 3, find three possible original problems.

Introduction to Linear Algebra 4
For which two numbers a will elimination fail on A = [:;]?

Introduction to Linear Algebra 4
For which three numbers a will elimination fail to give three pivots? 26 [ a 2 3] A = a a 4 is singular for three values of a.

Introduction to Linear Algebra 4
Look for a matrix that has row sums 4 and 8, and column sums 2 and s: " M . [a b] . atnx = c d a+b=4 a+c=2 c+d=8 b+d=s The four equations are solvable only if s = . Then find two different matrices that have the correct row and column sums. Extra credit: Write down the 4 by 4 system Ax = b with x = (

Introduction to Linear Algebra 4
Elimination in the usual order gives what matrix U and what solution to this "lower triangular" system? We are really solving by forward substitution: 3x = 3 6x +2y = 8 9x -2y + z = 9.

Introduction to Linear Algebra 4
reate a MATLAB command A(2, : ) = . " for the new row 2, to subtract 3 times row 1 from the existing row 2 if the matrix A is already known.

Introduction to Linear Algebra 4
Find experimentally the average 1 st and 2nd and 3rd pivot sizes from MATLAB 's [L, U] = lu(rand(3)). The average size abs(U(l, 1)) is above! because lu picks the largest available pivot in column 1. Here A = rand(3) has random entries between 0 and 1

Introduction to Linear Algebra 4
If the last comer entry is A(5, 5) = 11 and the last pivot of A is U(5, 5) = 4, what different entry A(5, 5) would have made A singular?

Introduction to Linear Algebra 4
Suppose elimination takes A to U without row exchanges. Then row j of U is a combination of which rows of A? If Ax = 0, is U x = O? If Ax = b, is U x = b? If A starts out lower triangular, what is the upper triangular U?

Introduction to Linear Algebra 4
Start with 100 equations Ax = 0 for 100 unknowns x = (Xl, ... ,XlOO). Suppose elimination reduces the 100th equation to 0 = 0, so the system is "singular". (a) Elimination takes linear combinations of the rows. So this singular system has the singular property: Some linear combination of the 100 rows