7. Let V be a complex vector space and let T e L(V). Let r be the minimal polynomial of T and suppose the degree of r is m. (a) Show that U = span {I,T,T²,T°,..T™-1} is an m-dimensional subspace of L(V). (b) Show that T™m e U. (c) If T is invertible, is T-1 e U?

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A: Let S={v1,v2,v3} represent the orthonormal basis for the subspace. By Gram Schmidt Process,…

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Q: Let W = {a + bx + cx + dx| a+ b = 0 and c – 3d = 0} be a subspace of P3 Then the dimension of W is…

A: Linear combination of vectors we use to find.

Q: 9. Find the orthogonal projection y of y = onto the subspace 2 0. W Span u = -3

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Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R. %3D

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A: The correct option is c . i.e. w is a subspace of ℝ3.

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A: This staement is true.

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Q: Suppose V is finite-dimensional and U and W are subspaces of V with W^0 ⊂ U^0. Prove that U ⊂ W.

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Q: Let W = {a + bx + cx² + dx³| c – 3d = 0 } be a subspace of P3. Then the dimension of W is equal to

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Q: is

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Q: 4) Let X, Y, Z be subspaces of a vector space V and assume that Y CX. Prove that Xn(Y+Z)% =Y+(XnZ).…

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Q: 12. Let K C R" and let V = {x € R" : x ly Vy E K}. Prove that V is a subspace of R".

A: " As per the company guidelines we are supposed to solve first question only. Kindly post the other…

Q: snip

A: We can represent the given set again as: W=xyz:x=3y+1 and z=-2y Let  w1=x1y1z1∈WThen,x1=3y1+1 and…

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Q: (5) Suppose that T E L(V) is such that all subspaces of V of dimension dim(V) – 1 are T-invariant.…

A: Please check step 2 for the solution.!

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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.