2. Let S, T,U be linear transformations such that (letting {u1, u2} or {u, , u2, uz} be bases of the vector spaces) S(u1) = S(u2) U1 + U2, U2, T(u1 T(u2) U(u1) U(u2) U(u3) u2 , 2u2, %3D U1 + U2 - Зиз Зиа - 2из - U3 %3D U2

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A: If F: U→V be an Inverse Linear Transformation such that                    F(F-1(u)) =F-1(F(u)) = u…

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A: (a) Given vectors are u1^→=1,0,0,1,u2^→=1,1,0,0,u3^→=0,0,1,1.   Consider U^=spanu1^→, u2^→, u3^→.…

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A: Let's find.

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A: Here is the solution of the given problem.

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A: Note: according to our guidelines we can answer only 11 th question

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A: Answer

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A:

Q: Find a basis of R that contains the vectors X = (1,1,1,1) and Y = (1,1,0,1).

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A: The answer is given in this below photo

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.