True or False? determine whether each statement is true or false. If a statement

Question

True or False? determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. (a) The determinant of a 2 times 2 matrix A is a_21a_12 - a_11a22 (b) The determinant of a matrix of order 1 is the entry of the matrix. (c) The ij-cofactor of a square matrix A is the matrix defined by deleting the ith row and jth column of A.

Explanation / Answer

(a). The statement is false. The value of the determinant is –(a21a12-a11 a22).

(b). The statement is false. The ijth minor M ij of a square matrix A is the determinant defined by deleting the ith row and the jth column of A. The cofactor of an element aij of a matrix A, written as Cij is defined as (1)i+j Mij.

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