Week 1

Question 1

Define a solution.

Answer 1

A pair (x0, y0) of real numbers is a solution to the equation ax + by = c
if setting x = x0 and y = y0 makes the equation true. That is if ax0 + by0 = c.

Question 2

Define the solution set.

Answer 2

The set of all solutions to the equation is called its solution set.

Question 3

What is an augmented matrix?

Answer 3

A matrix formed from a system of linear equations.

Question 4

Define ERO’s.

Answer 4

Elementary Row Operations.
1. Multiply a row by a non-zero constant.
2. Add a multiple of one row to another row.
3. Interchange two rows in the matrix.

Question 5

Define REF.

Answer 5

Row Echelon Form.
1. The first non-zero entry in each row is a 1 (called a Leading 1).
2. If a column contains a leading 1, then every entry of the column below the leading 1 is a zero.
3. As we move downwards through the rows of the matrix, the leading 1’s move from left to right.
4. Any rows consisting entirely of zeroes are grouped together at the bottom of the matrix.

Question 6

Give another name for a leading one.

Answer 6

A pivot.

Question 7

Define rank of a matrix.

Answer 7

Let A be a matrix. The rank of A, denoted rank(A) is the number
of leading 1’s in a row-echelon form obtained from A by Gaussian elimination.

Question 8

Define RREF.

Answer 8

Reduced row echelon form.
1. It is in row-echelon form, and
2. If a particular column contains a leading 1, then all other entries of that column are zeroes.

Question 9

Differentiate between leading and free variables.

Answer 9

The variables whose columns in the RREF contain leading 1’s are
called leading variables or pivot variables. A variable whose column in the RREF does not contain a leading 1 is called a free variable.

Question 10

Define matrix.

Answer 10

A rectangular array of numbers.