If A is diagonalizable and B is diagonalizable, must it be true that AB is diagonalizable? Give a proof or counterexample.

Q: et A be tx8 matrix. Knowing that Nullity (A) = 2. The %3D

A: In the given question, the concept of rank plus nullity theorem is applied. Rank plus Nullity…

Q: Show that matsix is not 15 diagonalizable A- 2 -3 2.

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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

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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: is not diagonalizable (by similarity) but is condiagonalizable. 4.6.P2 Show that (a) [ (b) [] is…

A: To show: (a) The matix i10i is not diagonalizable but it is condiagonalizable. (b) The matix 1-111…

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: A set of 5 vectors in R6 cannot be linearly independent. True False

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Q: Explain why S is not a basis for M22

A: We have t.o show that why S is not Basis for M2,2: Concept: The dimension of a vector space V, is…

Q: Suppose A is a 2x2 invertible Martix. Is the following statement true or false?  For each vector b,…

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Q: Use the concept of area of a parallelogram to write a statement about a 2 × 2 matrix A that is true…

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Q: Show that A + AT is symmetric for any square matrix A.

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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: The kernel of any invertible matrix consists of the zero vector only. True False

A: Given that  The kernal of any invertible matrix consists of the zero vector only

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

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Q: Show that the matrix is not diagonalizable.

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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: Prove that if a square complex matrix is unitarily diagonalizable, then it must be normal.

A: Every square complex unitarily diagonalizable matrix is normal. Let, A be a square complex unitarily…

Q: If both matrices A,B are orthogonal prove that (ab) is also orthogonal

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Q: (c) 0 is neither diagonalizable nor

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Q: Use the SVD to show that any square matrix A can be written as A = unitary and P is Hermitian. UP…

A: By SVD, we know that matrix A can be written as A=SDVTWhere S and V are orthogonal matrices andD is…

Q: Show that the diagonal entries of a Hermitian matrix must be real.

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Q: snip

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

Q: Let A be a real matrix such that the linear system Ax = 0 has a nonzero complex solution. Show that…

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Q: (Find the invers of the following matrix (If exists

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

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Q: Use Cramer's rule to compute the solutions of the following system:

A: We have to find the solutions of given system of equations.

Q: If d is a scalar multiple of b, then ax%. Select one: True False

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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: is represented in the standard bases by the matrix:

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Q: Show that if Aij is symmetric and Bij is skew-symmetric, then the scalar η given by η = AijBij is…

A: A tensor aij is said to be  symmetric if aij=aji. Similarly a tensor bij is said to be anti…

Q: Show that if M, - M. - (C ). (6 ). Ms - (: :). M2 = %3D %3D then the span of {M1, M2, M3} is the set…

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Q: List the Invertible Matrix Theorem statements that can be either all true or all false

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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: Explain why for any matrix A, AA' exists and prove that AA' is a symmetric matrix

A: Let A is any matrix of order m by n Am×n    and   Atn×m Now  AAt exists of order m by m To prove…

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

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Q: What must one do for the given matrix to be idempotent?

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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: Verify that P = is an orthogonal matrix. 1/32/3 N3

A: Given the matrix P=23-23132313-23132323We need to check whether the given matrix is orthogonal…

Q: How would you represent it in Basis 2?

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

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Q: Please show how to determine whether matrix A is diagonalizable: If possible, find an invertible P…

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

A: We have to check