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Please explain to me how we get the 4 x (7-4) in the solution I do not understand where it comes from. Photo 11 is the original question

Please explain to me how we get the 4 x (7-4) in the solution I do not understand where it comes from. Photo 11 is the original question

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please explain to me how we get the 4 x (7-4) in the solution I do not understand where it comes from. Photo 11 is the original question.

Given matrix is 20 0 4 4 7 2 -7 A = 20 0 0 then the determinant of the matrix is calculate by 7 2 1 8 cofactor method along the row 3 because there is onlyone non - negative element. So, det A = 2 × (-1)³+! (cofactor of element (3, 1)) + 0 x(-1)3+2 (cofactor of element (3, 2)) + 0 x (-1)3+3 (cofactor of element (3, 3)) + 0 x(-1)3+4 (cofactor of element (3,4)) = 2 x (cofactor of element (3, 1)) + 0 + 0 + 0 |0 0 4 = 2 x determinat of 7 2 -7 2 1 8 = 2 x (4 x (7 –- 4)) = 2× (12) = 24 where the element 2 x (-1)3+1 comes from the condition to find the determinant normally it is written as element x (-1)i+i, where i is row number and j is the column number of the element in the matrix.
Transcribed Image Text:Given matrix is 20 0 4 4 7 2 -7 A = 20 0 0 then the determinant of the matrix is calculate by 7 2 1 8 cofactor method along the row 3 because there is onlyone non - negative element. So, det A = 2 × (-1)³+! (cofactor of element (3, 1)) + 0 x(-1)3+2 (cofactor of element (3, 2)) + 0 x (-1)3+3 (cofactor of element (3, 3)) + 0 x(-1)3+4 (cofactor of element (3,4)) = 2 x (cofactor of element (3, 1)) + 0 + 0 + 0 |0 0 4 = 2 x determinat of 7 2 -7 2 1 8 = 2 x (4 x (7 –- 4)) = 2× (12) = 24 where the element 2 x (-1)3+1 comes from the condition to find the determinant normally it is written as element x (-1)i+i, where i is row number and j is the column number of the element in the matrix.
Compute the determinant by cofactor expansion. At each step, choose a row or column that involves the least amount of computation. 20 0 4 7 2 -7 20 0 0 7 2 1 8
Transcribed Image Text:Compute the determinant by cofactor expansion. At each step, choose a row or column that involves the least amount of computation. 20 0 4 7 2 -7 20 0 0 7 2 1 8
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