# Math 2B, College of the Desert

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1. Linear Equation
Linear Equation: x,y,z; more generally define a linear equation in the n variables x1, x2, . . . . , xn to be one that can be expressed in the form a1x1+a2x2+. . . +anxn.
2. Homogeneous Linear Equation
• Homogeneous Linear Equation:
• b = 0
• [in the variables x1,x2 . . .xn].
3. System of linear equations
System of linear equations: A finite set of linear equations or, more briefly, a linear system.
4. Variables
• Variables: Unknowns
• ie:
• x, y, z . . . . .
• or
• x1, x2, x3 . . . .
5. Ordered n-tuple
• Ordered n-tuple:
• (s1, s2, . . . . , sn)
6. N = 2
N = 2: Called an ordered pair, for ordered n-tuple.
7. N = 3
N = 3: Called an ordered triple, for ordered n-tuple.
8. Consistant
Consistant: Has at least one solution if not infinite.
9. Inconsistant
Inconsistant: Has no solutions.
10. Parameter
• Parameter: Substitution of a veriable with another (different) variable.
• ie:
• X = t
11. Parameter equations
Parameter equations: All the variables are substituted with a different variable (one not used yet).
12. Augmented Matrix
Augmented Matrix: Just putting the equations into matrix form.
13. Algebraic Operations
• Algerbraic Operations:
• 1. Multiply row by non-0 constant.
• 2. Interchange 2 rows.
• 3. Add a constant times 1 row to another.
14. Unique solution
Unique solution: One solution.
15. Theorem 1.4.1
• Theorem 1.4.1:
• c)A(BC)=(AB)C Associative Law Multi
• d)A(B+C)=AB+AC left distributive Multi
• e)(B+C)A=BA+CA Right distributive Multi
• f)A(B-C)=AB-AC
• g)(B-C)A=BA-CA
• h)a(B+C)=aB+aC
• i)a(B-C)=aB-aC
• j)(a+b)C=aC+bC
• k)(a-b)C=aC-bC
• l)a(bC)=(ab)C
• m)a(BC)=aB(C)=B(aC)
16. Theorem 1.4.2
• Theorem 1.4.2: If c is a scalar, and if the sizes of the matrix are such that the operations can be performed, then:
• a) A+0=0+A=A
• b)A-0=A
• c)A-A=A+(-A)=0
• d)0A=0
• e)If cA=0, then c=0 or A=0
17. Theorem 1.4.3
Theorem 1.4.3: If R is the reduced row echelon form of an nxn matrix A, then either R has a row of zeros or R is the Identity Matrix In.
 Author: Mattyj1388 ID: 81586 Card Set: Math 2B, College of the Desert Updated: 2011-06-23 22:26:48 Tags: Chapter1 math 2B Folders: Description: Elementary Linear Algerbra: Howard Anton / Chris Rorres Show Answers: