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:
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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.
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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.
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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:
- What is the difference between row echelon form and reduced row echelon form?
- How can you transform a matrix into its echelon form?
- Why is the echelon form important in solving systems of linear equations?
- What are the conditions for a matrix to be in reduced row echelon form?
- 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