Chapter 1.1

Question 1

A linear equation

Answer 1

A sum of variables with coefficients that are constants, without any products, roots or functions of the variables

Question 2

A homogeneous linear equation

Answer 2

A linear equation where the constant term is zero

Question 3

A solution to a linear system written on the form (s1, s2, … , sn)

Answer 3

An ordered n-tuple

Question 4

A linear system

Answer 4

A finite set of linear equations

Question 5

The possible amount of solutions a linear system can have

Answer 5

Zero, one or infinitely many

Question 6

Two things that define a linear system with no solutions

Answer 6

a) At least one equation have all coefficients set to 0 equaling a non-zero constant, after Gauss-Jordan elimination.
b) The linear equations have no common intersection.

Question 7

Two things that define a linear system with one solution

Answer 7

a) Gauss-Jordan elimination returns the identity matrix.

b) The linear equations intersect at a point.

Question 8

Two things that define a linear system with infinitely many solutions

Answer 8

a) After Gauss-Jordan elimination at least one variable have to be expressed by a function of at least one other variable.
b) The common intersection is a subspace of order n>1.

Question 9

The name of a linear system expressed through a rectangular array

Answer 9

Augmented matrix

Question 10

The three elementary row operations

Answer 10

a) Multiply a row through a nonzero constant.
b) Interchange two rows.
c) Add a constant times one row to another.