Linear algebra II

Question 1

Elementary row operations of matrix

Answer 1

for a mxn matrix A:
(1) interchanging any two rows of A;
(2) multiplying any row of A by a nonzero scalar;
(3) adding any scalar multiple of a row of A to another row
we refer to each of these operations as Type 1 Type 2 or Type 3 respectively

Question 2

Reduced row echelon form

Answer 2

Any matricies is in rref if the 3 properties are statisfied
(a) Any row containing a nonzero entry precedes any row in which all the entries are zero (if any).
(b) The first nonzero entry in each row is the only nonzero entry in its column.
(c) The first nonzero entry in each row is 1 and it occurs in a column to the right of the first nonzero entry in the preceding row.
The first nonzero entry in each row is called a pivot, and the column containing it is
called a pivot column