9780070109100, Chapter 5

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Chapter 5.2, Problem 3E Step-by-step solution Step of 6 Determinant of a matrix is the value that can be determined from the elements of a square matrix. Determinant of a matrix is written as det (A) or the symbol It is calculated by the following formula: a₁₁ a₂₃ Step 2 of 6 A minor of a matrix is the obtained by removing a row and a column from the given matrix and calculating the determinant of any smaller square from the remaining rows and column. A co-factor of a matrix is obtained by alternatively changing signs (row-wise, starting with no change of sign) of the elements of minor of that particular matrix. Step 3 of 6 The following determinant is given: a b Step 4 of 6 The minor of the element 'a' (Ma) is calculated as follows: Ma = e = The cofactor of the (Ca) is calculated as follows: =exi-fxh = Step 5 of 6 The minor of the element 'b' (Mb) is calculated as follows: Ma = g =dxi-fxg = di-fg The cofactor of the element 'b' (Cb) is calculated as follows: = = fg-di Step 6 of 6 The minor of the element 'f (Mf) is calculated as follows: = ab =axh-bxg = ah-bg The cofactor of the element (Cf) is calculated as follows: =