Pregunta
Let \( A \) be a \( 3 \times 6 \) matrix. What are the maximum and minimum values for the rank of \( A \) ? Maximum rank of \( A= \) Ex: 5 Minimum rank of \( A= \) Ex: 5
Ask by Gray King. in the United States
Feb 28,2025
Solución de inteligencia artificial de Upstudy
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The maximum rank of matrix \( A \) is 3, and the minimum rank is 0.
Solución
A is a 3 × 6 matrix. The rank of a matrix cannot exceed the minimum of the number of its rows and columns, so the maximum possible rank is min(3, 6) = 3.
The minimum rank of any matrix is 0 (achieved, for example, by the zero matrix).
Thus, the maximum rank of A is 3, and the minimum rank of A is 0.
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The maximum rank of a \( 3 \times 6 \) matrix \( A \) is determined by the smaller of the number of its rows and columns. Since there are 3 rows, the maximum rank is \( 3 \). The minimum rank of a matrix is \( 0 \), which occurs when all entries are zero. Therefore, for matrix \( A \), the minimum rank is \( 0 \).
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