Prove that if T is diagonalizable then T is diagonalizable.

Q: If A is diagonalizable and B is diagonalizable, must it be true that AB is diagonalizable? Give a…

A: If A is diagonalizable and B is diagonalizable then it is not necessary for AB to be diagonalizable.…

Q: 2 If A is diagonalizable then A is diagonalizable. Select one: O True False

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Q: IfQ is diagonalizable, then AT also diagonalizable. إختر واحداً:

A: We need to check whether if A is diagonalizable, then A is also diagonalizable.

Q: Determine whether th e set ẞ is a basis for the vector space V                           V = P 2,ẞ=…

A: ẞ comprises of the vectors 1 and 1 + 2x + 3x2

Q: Prove that if A is invertible and diagonalizable, then A-1 is also diagonalizable.

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Q: If A is diagonalizable then A´is diagonalizable. Select one: O True False

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Q: (12) Let T be a diagonalizable linear operator on V-finite dimensional, and let m be any positive…

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Q: (c) Let V and W be given as above. By using linear extension method, determine whether V is…

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Q: If V is a 7-dimensional vector space and S is a set of 10 vectors, then the elements of S must be…

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Q: Prove that a subset of a linearly independent vector set is linearly independent.

A: First of all,Let the set S= {v1, v2, v3, ……, vn} be a linearly independent set.Now, it is required…

Q: Show that W is a vector space.

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Q: ) Find the representation [T]B of T relative to the basis B'. Use [T]B to verify that T is…

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Q: Prove that if u and v are vectors in an inner product space such that ||u|| ≤ 1 and ||v|| ≤ 1, then…

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Q: Prove that if A is diagonalizable, so is AT.

A: Given: Matrix A is diagonalizable. To prove: AT is diagonalizable. Concept Used:1) If a matrix A is…

Q: Prove that k(x,x)=xAx' is a valid kernel, where A is a symmetric positive semidefinite matrix.

A: Let  we consider      kx,x' = xTAx'…

Q: Show that if A is both diagonalizable and invertible, so is A-1.

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Q: Let S be a maximal linearly independent subset of a vector space V. That is, S has the property that…

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Q: In part (a.) wouldn't you have to prove that U = Span(B) as well as B being linearly independent to…

A: Yes, we need to show both the parts. And the question you asked has already been proved in the…

Q: Every linearly dependent subset of a vector space V contains the zero vector. O True False

A: We have to see the given statements is true or false.

Q: Suppose v1, v2, v3, v4 span a vector space ?. Prove that the list v1 − v2, v2 − v3, v3 − v4, v4 also…

A: Let V be the vector space Since v1,v2,v3,v4 span the vector space V.

Q: If A is diagonalizable then A is diagonalizable. Select one: True False

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Q: Let W be the set of all vectors with x and y real. Find a basis of W1 x + y,

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Q: Let V be an n-dimensional vector space. Prove that any system {vi,...ūn} of linearly independent…

A: Let V be an n-dimensional vector space. We have to prove that any system v1→,v2→,v3→,.....,vn→ of…

Q: Determine if S is a subset of V where V = R3 is a vector space.

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Q: Describe all linear operators T on R2 such that T is diagonalizable and T3 - 272 +T= To.

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Q: Which row operations are normal operators? If a row operation is not a normal operator, given an…

A: An operator A : Rn ➞ Rn is called normal operator iff it satisfies : AA* = A*A Where A* is the…

Q: Find a basis as well as the dimension of the kernel and the image of each linear mapping

A: The given matrix is A=12012-12-11-32-2.

Q: Find the dimension of the vector space.R6

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Q: Let T be a diagonalizable linear operator on   V -finite-dimensional, and let m be any positive…

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Q: Prove that if u is orthogonal to both v and w, then u is orthogonal to sv+tw for all scalars s and…

A: Given that u is orthogonal to both v and w.

Q: Prove that in a given vector space V, the additive inverse of a vector is unique.

A: Let v,t be a vector  space .To show : for each x∈V ,there exist uniquey∈V such that x+y=0Proof :…

Q: If A is invertible and diagonalizable, then A also is diagonalizable. Select one: O True O False

A: Solve for true or false

Q: Let B be a basis for a vector space V. Then vectors u, v, w in V are linearly independent if and…

A: Let V be a vector space of dimension n with basis B=b1, ⋯, bn. Let u=u1b1+⋯+unbn, then the…

Q: Determine whether these vectors are a basis for R' by checking whether the vectors span R', and…

A: Introduction: For a vector space V, a set of vectors B is referred to as a basis for V if B spans V…

Q: Prove that Vn(I) is a vector space

A: Prove that VnI is a vector space.

Q: Suppose A and B are both orthogonally diagonalizable and AB = BA. Explain why AB is also…

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Q: Determine the basis that generates the following vector space by clearing the variable y: M = {(x,…

A: A basis of a vector space is the collection of vector which is linearly independent and generate the…

Q: Prove that, if A is similar to B, and B is diagonalizable, then A is diagonalizable.

A: Given that A is similar to B and B is diagonalizable.  To find A is diagonalizable.

Q: Show that if A is both diagonalizable and invertible, then so What does it mean if A is…

A: Introduction: If matrix A is an invertible matrix then every eigenvalue of this matrix non-zero.

Q: Prove that if the columns of A are linearly indepen­dent, then they must form a basis for col(A).

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Q: Prove that if A is invertible and BA = CA, then B = C.

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Q: prove that A is invertible and A = B = C. %3D

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Q: Prove that  A + At is symmetric for any square matrix A.

A: Known facts:

Q: *** If A is diagonalizable then A is diagonalizable. Select one: O True O False

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Q: Prove that a set S is linearly dependent if and only if S = { 0 } or there exist distinct vectors v,…

A: Necessary part:

Q: Show that V and L(F, V) are isomorphic vector spaces

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Q: Prove that if T is diagonalizable then T is diagonalizable.

A: Let V be a vector space of dimension nand T:V→V be a linear transformation such that T is…

Q: Let u and v be vectors in an inner product space V. Prove that ||u + v|| = ||u − v|| if and only if…

A: Given: Let u and v be vectors in an inner product space V. Prove that  ||u + v|| = ||u − v|| if and…

Q: Let A= then A is diagonalizable. Select one: True False

A: We have to check