Expand det C across the first row to prove that det C = det A+det B, where [a₁₁ +b₁₁a₁₂+b₁₂_a₁3 + b₁3 a22 A23 a32 C= a21 a31 a33 911 912 913 a22 923 931 a32 933. A = 921 b₁ b₁₂ b₁3 B=a21 22 23 a31 a32 A33

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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Expand det C across the first row to prove that det C = det A+ det B, where
[a₁₁ +b₁₁a₁₂+b₁₂
a₁3 + b₁3
a21
a23
a31
A33
C=
a22
a32
12
911 912
a13
A = 9₂1 922 A23
a31 a32
a33
B=
=
b₁ b₁2 b₁3
11
a21 A22 A23
[a31 A32 A33
Transcribed Image Text:Expand det C across the first row to prove that det C = det A+ det B, where [a₁₁ +b₁₁a₁₂+b₁₂ a₁3 + b₁3 a21 a23 a31 A33 C= a22 a32 12 911 912 a13 A = 9₂1 922 A23 a31 a32 a33 B= = b₁ b₁2 b₁3 11 a21 A22 A23 [a31 A32 A33
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