A matrix is said to be in Echelon form if

answered

A zero rows, if any, occurs they should be below the non-zero rows

Marked out of

100

B. first non-zero elements in any non-zero is unity

Flag question

C. the number of zeros before the first non-zero element increases with the number

D. ALL

The correct answer is **D. ALL**.

Here's why:

1. **A zero rows, if any, occurs they should be below the non-zero rows**: This is true for a matrix in echelon form. Any rows consisting entirely of zeros are placed at the bottom of the matrix.

2. **The first non-zero elements in any non-zero row is unity**: This refers to the leading entry (also known as a pivot) in each row being 1, which is a requirement for reduced row echelon form but can also be applied to echelon form depending on context.

3. **The number of zeros before the first non-zero element increases with the row number**: This condition ensures that each leading 1 (or the first non-zero element in each row) is to the right of the leading 1 in the row above, which is a key characteristic of echelon form.

Since all three conditions are necessary for a matrix to be in echelon form, the correct answer is **D. ALL**.

Would you like further details or have any other questions?

Here are 5 related questions to expand on this concept:
1. What is the difference between row echelon form and reduced row echelon form?
2. How can you transform a matrix into its echelon form?
3. Why is the echelon form important in solving systems of linear equations?
4. What are the conditions for a matrix to be in reduced row echelon form?
5. Can every matrix be transformed into an echelon form? Why or why not?

**Tip:** When transforming a matrix into echelon form, it's often helpful to focus on creating zeros below each pivot to simplify the process.

Discover the conditions for a matrix to be in echelon form with a clear explanation. Learn why each condition is essential and how to transform matrices into echelon form. Ideal for college students studying linear algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation