Compute the determinant using cofactor expansion along any row or column that seems convenient.o o o aoob c0 de fgh ij

Given determinant is Since the first row contains 3 zeros so it is convenient…

Answered: Compute the determinant using cofactor…

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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Question

Compute the determinant using cofactor expansion along any row or column that seems convenient.
o o o a
oob c
0 de f
gh ij

Expert Solution

Step 1: determinant by cofactor method

Given determinant is $open vertical bar table row 0 0 0 a row 0 0 b c row 0 d e f row g h i j end table close vertical bar$

Since the first row contains 3 zeros so it is convenient to consider the first row for evaluating determinant.

$open vertical bar table row 0 0 0 a row 0 0 b c row 0 d e f row g h i j end table close vertical bar space equals space open parentheses 0 close parentheses space open vertical bar table row 0 b c row d e f row h i j end table close vertical bar space minus space open parentheses 0 close parentheses open vertical bar table row 0 b c row 0 e f row g i j end table close vertical bar space plus space open parentheses 0 close parentheses open vertical bar table row 0 0 c row 0 d f row g h j end table close vertical bar space minus space open parentheses a close parentheses open vertical bar table row 0 0 b row 0 d e row g h i end table close vertical bar$

$equals space minus space open parentheses a close parentheses open vertical bar table row 0 0 b row 0 d e row g h i end table close vertical bar$

$equals space open parentheses negative a close parentheses space open square brackets open parentheses 0 close parentheses open vertical bar table row d e row h i end table close vertical bar minus open parentheses 0 close parentheses open vertical bar table row 0 e row g i end table close vertical bar plus open parentheses b close parentheses open vertical bar table row 0 d row g h end table close vertical bar close square brackets$ ( again considered first row )

$equals space open parentheses negative a close parentheses open parentheses b close parentheses open vertical bar table row 0 d row g h end table close vertical bar$

$equals space open parentheses negative a close parentheses open parentheses b close parentheses open square brackets open parentheses 0 close parentheses open parentheses d close parentheses minus open parentheses d close parentheses open parentheses g close parentheses close square brackets$

$equals space open parentheses negative a b close parentheses open square brackets negative d g close square brackets$

$equals space a b d g$

$open vertical bar table row 0 0 0 a row 0 0 b c row 0 d e f row g h i j end table close vertical bar space equals space a b d g$