24. Let A [A₁, A2, A3] be a (3 × 3) matrix and set = 2 a) Show that B - 3 1 00 -1 ] 3 4 AB = [2A₁ + 3A2 + A3, -A2 + 3A3, 4A3]. b) Use column operations to show that det (AB) = -8 det (A). c) Conclude that det (AB) = det (A) det (B).
24. Let A [A₁, A2, A3] be a (3 × 3) matrix and set = 2 a) Show that B - 3 1 00 -1 ] 3 4 AB = [2A₁ + 3A2 + A3, -A2 + 3A3, 4A3]. b) Use column operations to show that det (AB) = -8 det (A). c) Conclude that det (AB) = det (A) det (B).
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
![24. Let A = [A₁, A2, A3] be a (3 × 3) matrix and set
200
a) Show that
B =
3 -1 0
1 3 4
AB = [2A₁ + 3A₂ + A3, −A2 + 3A3, 4A3].
b) Use column operations to show that
det (AB) = -8 det(A).
c) Conclude that det (AB) = det(A) det(B).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb989860-4d1c-4fb5-9e6b-42a4528dce9c%2Fb297c270-0c9f-4280-afa0-af86d03f162b%2F857adi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:24. Let A = [A₁, A2, A3] be a (3 × 3) matrix and set
200
a) Show that
B =
3 -1 0
1 3 4
AB = [2A₁ + 3A₂ + A3, −A2 + 3A3, 4A3].
b) Use column operations to show that
det (AB) = -8 det(A).
c) Conclude that det (AB) = det(A) det(B).
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