undefined Solution The value of the determinant | cosh t sin h t sin h t cosh t | . The value of the determinant | cosh t sin h t sin h t cosh t | is 1 _ . Definition used: A determinant of order n is a scalar associated with an n × n matrix A = [ a j k ] is denoted by, D = det A = | a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋅ ⋅ ⋯ ⋅ ⋅ ⋅ ⋯ ⋅ a n 1 a n 2 ⋯ a n n | The determinant is given by, D = a 1 k C 1 k + a 2 k C 2 k + ⋯ + a n k C n k Here C j k = ( − 1 ) j + k M j k where M j k is a determinant of order n − 1 which is the determinant of the sub matrix of A obtained from A by omitting the row and column of the entry a j k , that is the j th row and the k th column. Calculation: Given that the determinant is | cosh t sin h t sin h t cosh t | . It is observed that for a 2 × 2 matrix the determinant is given by, | a b c d | = a d − b c . Evaluate the determinant | cosh t sin h t sin h t cosh t | and the following is obtained. | cosh t sin h t sin h t cosh t | = cosh t ( cosh t ) − sin h t ( sin h t ) = cosh 2 t − sin h 2 t = 1 ( ∵ cosh 2 x − sin h 2 x = 1 ) Therefore, the value of the determinant | cosh t sin h t sin h t cosh t | is 1 _ .

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ISBN: 9780470458365

Author: Erwin Kreyszig

Publisher: Wiley, John & Sons, Incorporated

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