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In the complex field c is the given vector space over the real field. R and operator T on C is defined as T(z)=z( bar) .then the matrix of T w.r.t. the basis {1 I,1 2i} is Ans in matrix please?
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In the complex field c is the given vector space over the real field. ...
Matrix of Operator T w.r.t. the Basis {1 I, 1 2i}
Definition of Operator T
The operator T on C is defined as T(z) = z(bar), where z(bar) is the complex conjugate of z.
Basis of Vector Space C
The basis of vector space C over the real field R is {1, i}.
Coordinate Vectors of Basis
The coordinate vectors of the basis {1, i} w.r.t. the basis {1, i} are [1 0] and [0 1], respectively.
Extension of Basis to {1 I, 1 2i}
To extend the basis to {1 I, 1 2i}, we need to express 1 and i in terms of 1 I and 1 2i.
Expressing 1 and i in terms of 1 I and 1 2i
1 = (1/3)(3) = (1/3)(1 I + 2i(1 2i)) and i = (1/3)(3i) = (1/3)(1 I - 2i(1 2i)).
Coordinate Vectors of Basis w.r.t. {1 I, 1 2i}
The coordinate vectors of the basis {1 I, 1 2i} w.r.t. the basis {1 I, 1 2i} are [1 0] and [0 1], respectively.
Matrix of Operator T w.r.t. {1 I, 1 2i}
To find the matrix of operator T w.r.t. the basis {1 I, 1 2i}, we need to apply T to each basis vector and write the result in terms of the basis {1 I, 1 2i}.
T(1) = 1(bar) = 1, so [T(1)] = [1 0].
T(I) = I(bar) = 1 - i(1 2i) = 1 - i + 2, so [T(I)] = [-i+3 2].
Therefore, the matrix of operator T w.r.t. the basis {1 I, 1 2i} is
[1 0]
[-i+3 2].
Definition of Operator T
The operator T on C is defined as T(z) = z(bar), where z(bar) is the complex conjugate of z.
Basis of Vector Space C
The basis of vector space C over the real field R is {1, i}.
Coordinate Vectors of Basis
The coordinate vectors of the basis {1, i} w.r.t. the basis {1, i} are [1 0] and [0 1], respectively.
Extension of Basis to {1 I, 1 2i}
To extend the basis to {1 I, 1 2i}, we need to express 1 and i in terms of 1 I and 1 2i.
Expressing 1 and i in terms of 1 I and 1 2i
1 = (1/3)(3) = (1/3)(1 I + 2i(1 2i)) and i = (1/3)(3i) = (1/3)(1 I - 2i(1 2i)).
Coordinate Vectors of Basis w.r.t. {1 I, 1 2i}
The coordinate vectors of the basis {1 I, 1 2i} w.r.t. the basis {1 I, 1 2i} are [1 0] and [0 1], respectively.
Matrix of Operator T w.r.t. {1 I, 1 2i}
To find the matrix of operator T w.r.t. the basis {1 I, 1 2i}, we need to apply T to each basis vector and write the result in terms of the basis {1 I, 1 2i}.
T(1) = 1(bar) = 1, so [T(1)] = [1 0].
T(I) = I(bar) = 1 - i(1 2i) = 1 - i + 2, so [T(I)] = [-i+3 2].
Therefore, the matrix of operator T w.r.t. the basis {1 I, 1 2i} is
[1 0]
[-i+3 2].
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In the complex field c is the given vector space over the real field. R and operator T on C is defined as T(z)=z( bar) .then the matrix of T w.r.t. the basis {1 I,1 2i} is Ans in matrix please? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about In the complex field c is the given vector space over the real field. R and operator T on C is defined as T(z)=z( bar) .then the matrix of T w.r.t. the basis {1 I,1 2i} is Ans in matrix please? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the complex field c is the given vector space over the real field. R and operator T on C is defined as T(z)=z( bar) .then the matrix of T w.r.t. the basis {1 I,1 2i} is Ans in matrix please?.
In the complex field c is the given vector space over the real field. R and operator T on C is defined as T(z)=z( bar) .then the matrix of T w.r.t. the basis {1 I,1 2i} is Ans in matrix please? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about In the complex field c is the given vector space over the real field. R and operator T on C is defined as T(z)=z( bar) .then the matrix of T w.r.t. the basis {1 I,1 2i} is Ans in matrix please? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the complex field c is the given vector space over the real field. R and operator T on C is defined as T(z)=z( bar) .then the matrix of T w.r.t. the basis {1 I,1 2i} is Ans in matrix please?.
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