CONCEPTS

Question 1

What is an n-tuple?

Answer 1

order list of numbers. 3-tuple for example is 3 dimensional (x,y,z)

Question 2

what is an augmented matrix

Answer 2

a series of numbers that were converted from a system of linear equtions

Question 3

what is a linear equation

Answer 3

makes a straight line,
- no trig
- power of one
- no rational
- no log or exponential

Question 4

what are the three possibilities when it comes to the solution of a linear equation

Answer 4

All linear equations have either 1, infinite or zero solutions

Question 5

what is a consistent matrix?

Answer 5

one that has either 1 or an infinite number of solutions

Question 6

what is an inconsistent system of equations?

Answer 6

No solutions

Question 7

What are the 3 elementary row operations

Answer 7

1. you can interchange two rows
2. you can multiply a row with a non zero number
3. add a scalar multiple of one row to another

Question 8

what are the subscripts i and j?

Answer 8

they are i : rows
j: columns

Question 9

conditions for reduced echelon form matrix?

Answer 9

1. first row left has to be 1
2. all number under leading 1 must be zero
3. the next leading 1 in succesive rows must be further to the right than one above
4. if row is all zeros, then must be grouped at bottom
5. zeros above leading 1s

Question 10

how to know if there is one solution

Answer 10

same number of variables as # of leading 1s

Question 11

how to know if there are 0 solutions

Answer 11

leading 1 in constants

Question 12

how to know that there are infinity soln

Answer 12

less leading ones than free variables

Question 13

What is a homogeneous linear system

Answer 13

All constant terms are zero, always has a trivial solution.

Question 14

what is a trivial solution?

Answer 14

• means all variables are equal de zero

Question 15

what is a pivot row or column

Answer 15

contains a leading 1