Math Problem Statement

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

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

D. ALL

Solution

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.

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Math Problem Analysis

Mathematical Concepts

Matrices
Echelon Form
Linear Algebra

Formulas

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Theorems

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Suitable Grade Level

College