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Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that the area(a, a + b) = area(a, b). (b.) Verify the statement in (a.) when a = (2, 1) and b = (-2,4). (c.) Determine the area(3a, 26) in terms of area(a, b).

Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that the area(a, a + b) = area(a, b). (b.) Verify the statement in (a.) when a = (2, 1) and b = (-2,4). (c.) Determine the area(3a, 26) in terms of area(a, b).

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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1. Let a = (a1, a2), b = (b1,b2) be vectors in R². The area(a, b) is given by a1b₂-a2b₁. (a.) Show that the area(a, a + b) = area(a, b). (b.) Verify the statement in (a.) when a = (2, 1) and b = (-2,4). (c.) Determine the area(3a, 26) in terms of area(a, b). (d.) Determine the area(a, a + 2b) in terms of area(a, b).
Transcribed Image Text:1. Let a = (a1, a2), b = (b1,b2) be vectors in R². The area(a, b) is given by a1b₂-a2b₁. (a.) Show that the area(a, a + b) = area(a, b). (b.) Verify the statement in (a.) when a = (2, 1) and b = (-2,4). (c.) Determine the area(3a, 26) in terms of area(a, b). (d.) Determine the area(a, a + 2b) in terms of area(a, b).
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