Question

In echelon form, which of the following is incorrect?

• A. Every row of $A$ which has all its entries $0$ occurs below every row which has a non-zero entry.
• B. The first non-zero entry in each non-zero row is $1$.
• C. The number of zeros before the first non-zero element in a row is less than the number of such zeros in the next row.
• D. Two rows can have same number of zeros before the first non-zero entry.

Answer 1

Answer: (A), (D)

The correct options are
A Every row of $A$ which has all its entries $0$ occurs below every row which has a non-zero entry.
D Two rows can have same number of zeros before the first non-zero entry.

By the properties of echelon form ,

A row which has all its entities $0$ can occur above the row which has a non zero entity.

Two rows can have same number of zeros before the first non zero entity

Therefore option $A$ and $D$ are incorrect statements