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

Q: Let A be a matrixand x be a vector given as follows

A:

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: If each component of a vector in R³ is doubled, the L2 norm of that vector is doubled True False

A: To give answer in true or false of the statement.

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

A:

Q: (a) Find the orthogonal complement S+.

A: Orthogonal complement:- let VF be an inner product space and S be a subspace of V.the orthogonal…

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: Let M,xn be a set of squarenx n-matrices. Is the set Mnxn a vector space? Explain. Find 2 different…

A: We find two different basis of M_2×2

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

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Q: we that Al are matrix norm

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Q: a Let A = b - a then A is diagonalizable. b Select one: O True O False

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Q: Let B be a bxb matrx and Ca ): A-1)(X-メーい(メ) If the rame of I-B is at most 2, the 4) the rows of…

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Q: Provide a set four vectors in R³ that are not pairwise orthogonal and an orthogonalisation of the…

A: Let s=1,1,1,1,0,1,0,1,1,1,1,0be aset of four vectors in R3 such thateach vector of s are not…

Q: (b) Find the orthogonal decomposition of v with respect to W. projw(v): %3D perpw(v)

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

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Q: Consider the linear operator L: BC[0, ] → BC[0, 7] defined by Си — и" - 2и is unbounded in the sup…

A: Consider the linear operator L:BC0,π→BC0,π defined by: Lu=u''-2u. We know that the set BC0,π is…

Q: Find a basis fo

A: Given,            A=3-916-26-161-38

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

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Q: If A is symmetric and invertible and has an LDU factorization, show that U = LT

A: To show: If A is symmetric and invertible and has an LDU factorization, show that U = LT.

Q: , counting the multiplicities. Then A is orthogonally diagonalizable.

A: We have to examine that matrix A is orthogonally diagonalizable or not.

Q: |A student writes the statement ā.b = b.č and then concludes that a = č. Construct a simple…

A: The given problem is related to vectors. Given: a student writes the statement a→ . b→ = b→ . c→ and…

Q: (2) Prove that if a + b and a – b are orthogonal, then a and b have the same magnitude.

A:

Q: snip

A: Given Orthogonally diagonalize A=abba,If b not equal to zero

Q: 2rị + 13 T: R' → R?, T 21, 22, 13, L4 ER -12 - 3r4

A: Given  and the standard bases are given by

Q: 4 コ 2 %3D 1

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Q: Prove that if {u, v} is linearly independent, then so too is {u+ v, u - v}.

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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 W = Span in W+ (the orthogonal complement to W)?

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Q: Let z = 6. and y Find the vectori = 47 - 7j and its additive inverse.

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

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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: Find the norm of U = V + 3W V(9 , 10 , 1) and W(8, -4,-9)

A: The given two vectors are V=(9, 10, 1) and W=(8, -4, -9). Evaluate U as follows. U=V+3W=9, 10, 1+38,…

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: show that if A cnal B are on singu lar (AB)=B A matricesythen %3D

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

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Q: Show that a. A is diagonalizable if (a – d)² + 4bc > 0. b. A is not diagonalizable if (a – d)² + 4bc…

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Q: Suppose A is invertible and orthogonally diagonalizable. Explain why A–1 is also orthogonally…

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Q: Prove that if A is not square, then either the row vectors of A or the column vectors of A form a…

A: Suppose A is an x×y matrix that is not square. Either A has more rows than column (x>y) or more…

Q: If A ER2X2 is not diagonalizable, then A is not diagonalizable. True or False? Give an example to…

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Q: determine if the vector v is a linear combi­nation of th e remaining vectors.

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Q: suppose that u, v, and ware vectors in an inner product space such that  <u,v> = 1,…

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

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Q: f A E R2x2 is not diagonalizable, then A is not diagonalizable. True or False? Give an example to…

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Q: Let A = Show that A can be diagonalised. Then, compute A°.

A: The solution of the problem is given in the next steps.

Q: Find the orthogonal projection of v=2 onto W.

A:

Q: suppose that u, v, and ware vectors in an inner product space such that  <u,v> = 1,…

A: We have given u,v=1,u,w=5,v,w=0,u=1,v=3,w=2  We have to calculate 2u-3v+w

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

A: Given T be a linear operator on a vector space V and W be a T-invariant subspace of V. Define a…

Q: If two Hermitian operators A and B commute, show that they can be simultaneously diagonalized.

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

A: We have to check

Q: Let B = {v1, .. be a linearly independent set in Rn. Explain why B must be a basis for TR"

A: