Mathematics · Linear Algebra

Let A be an m × n matrix. Let A(1, :), A(:, 1), and A(1, 1) be the matrices obtained from A by deleting row 1, deleting column 1, and deleting both row 1 and column 1 respectively. Which of the following inequalities always holds?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

rank(A) - 2 ≤ rank A(1, 1) ≤ rank(A)

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Let A be an m &times; n matrix. Let A(1, :), A(:, 1), and A(1, 1) be the matrices obtained from A by deleting row 1, deleting column 1, and deleting both row 1 and column 1 respectively. Which of the following inequalities always holds?