4. Let A be an m x n matrix, with m

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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4. Let \( A \) be an \( m \times n \) matrix, with \( m < n \), which after being put in reduced echelon form is shown to have exactly two non-pivot variables. Then:

a. The system of equations \( A \mathbf{x} = \mathbf{b} \) cannot have a unique solution

b. \(\text{rank}(A) = n - 2\)

c. \( m \geq n - 2\)

d. All of the above
Transcribed Image Text:4. Let \( A \) be an \( m \times n \) matrix, with \( m < n \), which after being put in reduced echelon form is shown to have exactly two non-pivot variables. Then: a. The system of equations \( A \mathbf{x} = \mathbf{b} \) cannot have a unique solution b. \(\text{rank}(A) = n - 2\) c. \( m \geq n - 2\) d. All of the above
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Step 1

Given A is m×n matrix with m<n  and have exactly 2 non-pivot variable.

ie, number of pivot column is =n-2

 

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