Exam 1

Question 1

Linear Equation

Answer 1

Can be written in the form a1x1 + aNxN = b

Question 2

System of Linear Equation

Answer 2

A collection of one or more linear equations involving the same variables

Question 3

Solution

Answer 3

List of numbers that makes each equation a true statement

Question 4

Solution Set

Answer 4

A set of all possible solutions

Question 5

Consistent

Answer 5

One solution or infinitely many

Question 6

Inconsistent

Answer 6

No solution

Question 7

Reduced row echelon form

Answer 7

The leading entry in each non-zero row is one and each leading one is the only non-zero entry in its column

Question 8

pivot position/column

Answer 8

Location in A that corresponds to a leading 1 in the reduced echelon form of A

Question 9

Free variable

Answer 9

Aren’t in pivot columns

Question 10

Linear combination

Answer 10

y = c1v1 + cPvP where c are scalars and v are vectors

Question 11

Homogeneous

Answer 11

Ax=0 where A is (m x n) and 0 is the zero vector in Rn

Question 12

Trivial Solution

Answer 12

When Ax = 0 has at least one solution

Question 13

NonTrivial

Answer 13

Non-zero vector x that satisfies Ax = 0

Question 14

Parametric vector form

Answer 14

Whenever a solution set is described explicitly with vectors

Question 15

Linearly Independent

Answer 15

Has the trivial solution: x1v1 …xPvP = 0

Question 16

Linearly Dependent

Answer 16

When the weights are not all zero

Question 17

Dependence Relation

Answer 17

When the weights are not all zero

Question 18

Linear Transformation

Answer 18

Any matrix transformation

Question 19

Standard Matrix

Answer 19

A=[T(e1) … T(eN)]

Question 20

Onto

Answer 20

Range = domain and pivot in all rows

Question 21

1 - 1

Answer 21

T(u) = T(v) and pivot in all columns

Question 22

Matrix Inverse

Answer 22

CA = I and AC = I

Question 23

Uniqueness of REF Theorem

Answer 23

Each matrix is row equivalent to one and only one REM

Question 24

Existence and Uniqueness Theorem

Answer 24

If the rightmost column is not a pivot then the solution is consistent