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Let x = (₁, 2, 3) € C³ be any vector and let a = (a1, a2, as), b = (b₁,b2, b3) C3 be fixed. Let 1 b₁ 12 b₂ х3 b3 a1 T(x) = det (a | x | b ) = det a2 az a) Find T(2e1) where e₁ is the first standard basis vector in C³. b) Use the symbol T(x) to explain what it means that the determinant of 3 x 3 matrix is a linear map with respect to the second column.

Let x = (₁, 2, 3) € C³ be any vector and let a = (a1, a2, as), b = (b₁,b2, b3) C3 be fixed. Let 1 b₁ 12 b₂ х3 b3 a1 T(x) = det (a | x | b ) = det a2 az a) Find T(2e1) where e₁ is the first standard basis vector in C³. b) Use the symbol T(x) to explain what it means that the determinant of 3 x 3 matrix is a linear map with respect to the second column.

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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Needed to be solved a and b parts correctly in 15 minutes and get the thumbs up please show neat and clean work Please do it asap Thanks in advance
Let x = (1, 2, 3) EC³ be any vector and let a = (a₁, a2, a3), b = (b₁,b2, b3) € C³ be fixed. Let a1 x1 b₁ x2 b2 I3 ba T(x) = det (a | x | b ) = det a2 az a) Find T(2e1) where e₁ is the first standard basis vector in C³. b) Use the symbol T(x) to explain what it means that the determinant of 3 x 3 matrix is a linear map with respect to the second column.
Transcribed Image Text:Let x = (1, 2, 3) EC³ be any vector and let a = (a₁, a2, a3), b = (b₁,b2, b3) € C³ be fixed. Let a1 x1 b₁ x2 b2 I3 ba T(x) = det (a | x | b ) = det a2 az a) Find T(2e1) where e₁ is the first standard basis vector in C³. b) Use the symbol T(x) to explain what it means that the determinant of 3 x 3 matrix is a linear map with respect to the second column.
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