Let A be an n xn matrix. Determine whether the statement below is true or false. Justify the answer. An nxn determinant is defined by determinants of (n - 1)x (n – 1) submatrices. Choose the correct answer below. O A. The statement is false. An nxn determinant is defined by determinants of (n - 1)x (n – 1) submatrices only when n> 3. Determinants of 1x1, 2x2, and 3x3 matrices are defined separately. O B. The statement is false. Although determinants of (n - 1)x (n - 1) submatrices can be used to find nxn determinants, they are not involved in the definition of nxn determinants. O C. The statement is true. The determinant of an nxn matrix A can be computed by a cofactor expansion across any row or down any column. Each term in any such expansion includes a cofactor that involves the determinant of a submatrix of size (n - 1)x (n - 1). O D. The statement is true. The determinant of an nxn matrix A can be computed by a cofactor expansion along either diagonal. Each term in any such expansion includes a cofactor that involves the determinant of a submatrix of size (n - 1)x (n – 1).

Let A be an n xn matrix. Determine whether the statement below is true or false. Justify the answer. An nxn determinant is defined by determinants of (n - 1)x (n – 1) submatrices. Choose the correct answer below. O A. The statement is false. An nxn determinant is defined by determinants of (n - 1)x (n – 1) submatrices only when n> 3. Determinants of 1x1, 2x2, and 3x3 matrices are defined separately. O B. The statement is false. Although determinants of (n - 1)x (n - 1) submatrices can be used to find nxn determinants, they are not involved in the definition of nxn determinants. O C. The statement is true. The determinant of an nxn matrix A can be computed by a cofactor expansion across any row or down any column. Each term in any such expansion includes a cofactor that involves the determinant of a submatrix of size (n - 1)x (n - 1). O D. The statement is true. The determinant of an nxn matrix A can be computed by a cofactor expansion along either diagonal. Each term in any such expansion includes a cofactor that involves the determinant of a submatrix of size (n - 1)x (n – 1).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 32E

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