If a linear system has four equations and seven variables,
then it must have innitely many solutions.
If a linear system has seven equations and four variables,
then it must be inconsistent.
If a linear system has the same number o
If u1, u2, . . . , um are vectors and c1, c2, . . . , cm are scalars, then
11 + 22 + +
is a linear combination of the vectors.
- Let cfw_1, 2, . . . , be a set of vectors in . The span of this set is denoted spancfw_1,
1) Determine if T is ivertible, and if so, find T-1.
([ ]) [ ]
x 1 + x 2+ x 3
T x 2 = x2 + x 3
x 1x 2+ x3
1 1 1
A= 0 1 1
1 1 1
By definition, if det ( A )=0, then the matrix A is not invertible.
det ( A )=( 1 ) ( (11 )(11 ) ) (1 ) (
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Week 1.5 Syllabus: Systems of Linear Equations
(1) System of linear equations: m linear equations n=1 aij xj = bi for i = 1, . . . , m j in n unknowns x1 , . . . , xn ; called homogeneous if all bi = 0. A = [aij ] is the matrix of
coecients, [A b] is t
WeBWorK assignment number W1F09 is due : 09/03/2009 at 09:00am EDT. The (* replace with url for the course home page *) for the course contains the syllabus, grading policy and other information.
This le is /conf/snippets/setHead
1.3 # 12ad For something like (a, b+c-2a, c-b,c) write it as a(1,-2,0,0) +
b(0,1,-1,0) + c(0,1,1,1) and recognize the set as all linear combinations
of 3 vectors [next week we will see that ANY span of a collection of vectors
forms a subspace, but here
The common textbook Hmwk # 1 for the three sections due next Wednesday
at 5pm is listed below, including comments from Professor McCrimmon to
his section which apply across all three sections. The Webwork Set # 1,
due next Wednesday by