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)| -3,3 2 9 -3 = 2 = 2(1) || 0 0 0 = 2 2( expand along C₁ 0 21 0 = 20 -1 N -4 1 5 3 1 -2 1 4 2 x 7 -4 1 -1 5 4 -3 2 -1 1 9 -3 1 -2 1 2 R₂ - 2 R₁ R3 + R₁ R4 + 3 R₁ expand (along C₁) R₁ + 4 R₂ R3-5 R₂.

)| -3,3 2 9 -3 = 2 = 2(1) || 0 0 0 = 2 2( expand along C₁ 0 21 0 = 20 -1 N -4 1 5 3 1 -2 1 4 2 x 7 -4 1 -1 5 4 -3 2 -1 1 9 -3 1 -2 1 2 R₂ - 2 R₁ R3 + R₁ R4 + 3 R₁ expand (along C₁) R₁ + 4 R₂ R3-5 R₂.

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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)| -3,3 2 9 -3 = 2 11 0 0 0 = 2( expand along C₁ O 0 = 20 N = 2(1) 1 -1 3 -4 1 -1 Y 1 5 4 1 -2 1 5 4 2 -4 21 -1 319 - -3 2 1 9 -3 x -2 1 2 R₂ - 2 R₁ R3 + R₁ R4 + 3 R₁ expand (along C₁) R₁ + 4 R₂ R3-5 R₂.
Transcribed Image Text:)| -3,3 2 9 -3 = 2 11 0 0 0 = 2( expand along C₁ O 0 = 20 N = 2(1) 1 -1 3 -4 1 -1 Y 1 5 4 1 -2 1 5 4 2 -4 21 -1 319 - -3 2 1 9 -3 x -2 1 2 R₂ - 2 R₁ R3 + R₁ R4 + 3 R₁ expand (along C₁) R₁ + 4 R₂ R3-5 R₂.
If we want to be really creative (and efficient), we can use a combination of row/column operations and cofactor expansion to compute the determinant of a square matrix: Example: Evaluate the determinant of 2 5 NO 7 0 1 -2-3 4 2 2 0 -2 4 2 5 1 -29 -23 NOW -3 9 -13 2 2 3 4 0 -7 -2 19 = 0 2 9 13 14 2 6 4 7 2 -7 -2 13 6 = 2 = 2 0-3 10 0 2 3 7 0 -1 -1 -4 -3 -1 -5 -10 4 6 12 2 0 9 3 4 19 14 -29 4 -23 -13 720 1 2 3 0 7 -1 -1 -4 -3 -3 -1 -5 1 2 3 0 1 -1 -4 1 5 9 -13 4 6 4 st -10 4 -2 1 2 R3 + R₁ R4-2 R₁ R₁ - R₁ expand along C₁ R₂-2 R₁ R3 + R₁ R4 + 3 R₁
Transcribed Image Text:If we want to be really creative (and efficient), we can use a combination of row/column operations and cofactor expansion to compute the determinant of a square matrix: Example: Evaluate the determinant of 2 5 NO 7 0 1 -2-3 4 2 2 0 -2 4 2 5 1 -29 -23 NOW -3 9 -13 2 2 3 4 0 -7 -2 19 = 0 2 9 13 14 2 6 4 7 2 -7 -2 13 6 = 2 = 2 0-3 10 0 2 3 7 0 -1 -1 -4 -3 -1 -5 -10 4 6 12 2 0 9 3 4 19 14 -29 4 -23 -13 720 1 2 3 0 7 -1 -1 -4 -3 -3 -1 -5 1 2 3 0 1 -1 -4 1 5 9 -13 4 6 4 st -10 4 -2 1 2 R3 + R₁ R4-2 R₁ R₁ - R₁ expand along C₁ R₂-2 R₁ R3 + R₁ R4 + 3 R₁
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