4. Let B be the a basis of R², and let L: R² R² be the linear operator with the matrix |(4) 8 = 1 3] -3 12 Find a matrix P that diagonalizes the matrix [L]B. Hint: note that the eigenvalues of [L]g are 9 and -9.

Q: -11 is a vector in the standard basis of R². 9.

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Q: Am.111.

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Q: Let A be a 3 x 3 matrix such that B Find a non-zern vector Null(AT) -5 is a basis of Col(A).

A: Given : Let A be a 3×3 matrix and  B=5-5-2 , -54-2 be the basis of ColA To Find : A non-zero vector…

Q: Which of the following sets are closed under addition? (i) The set of all vectors in R² of the form…

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Q: Let the n dimensional square matrices A and B be similar, i.e., PBP-¹. where P is a n dimensional…

A: The n dimensional square matrices A and B be similar. i.e., A=PBP-1, where P is a n dimensional…

Q: (b) Find a complete orthonormal set of eigenvectors {v1, v2, V3}, where v; is an vector for A;.…

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Q: 6. For the matrix A, find: a) all the eigenvalues, b) all eigenvectors, and c) an orthogonal matrix.…

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Q: -61 2 Let A = Find all (real) eigenvalues for A. Then find a basis of each eigenspace, and…

A: To diagonalize it.

Q: Find a basis {b₁,b2,...} for the eigenspace corresponding to (the eigenvalue) X. -15 -32 -18 12 -56…

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Q: -3 -3 0 0 -3 -3 0 0 0 0 -3 -3 0 0 -3 -3 Find the eigenvalues and an orthonormal basis for each…

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Q: What are the eigenvalues and normalized eigenvectors of the operator: F = Aô, + Bôz Here A and B are…

A: Given, F^=Aσy^+Bσz^....(1) Where, σy^=0-ii0σz^=100-1 Then from the equation (1),…

Q: 3 3 12. Given matrix A = -5 3 3 A) Determine the diagonalization B) Find another diagonalization of…

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Q: Find a basis {b₁,b2,...} for the eigenspace corresponding to (the eigenvalue) X. -25 -15 -9 27 17 9…

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Q: Suppose the matrix A is used to transform points in the plane iteratively. That is, given a point v,…

A: Given that A and B are similar matrices, and given that A=SBS-1 Now, λ is an eigen value of A and v…

Q: Suppose {u₁, U2,..., U2n} is an orthonormal basis for R2n. Let n A = Im - Σuju?. j=1 Show that (a)…

A: We show that A is idempotent matrix   For this we have A2 =A .. And the eigen values of idempotent…

Q: Suppose that a matrix A has the following eigenvalues and eigenvectors: T • λ=−1haseigenvectorx=[1,…

A: Given: The eigenvalues and eigenvectors of the matrix are as follows, • λ=−1 The  eigen vector…

Q: Exercise 2. Suppose that A and B are matrices of the same size. Prove the following: (a) (aA)¹ = aAª…

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Q: Find a basis of the eigenspace associated with the eigenvalue −1−1 of the matrix.

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Q: 5. Consider the space {) a a + b+c= d : 2a + b = d a + b+ 3c = 0 H = CRª. C d (a) Find a matrix A…

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Q: Explain how to find a basis for the eigenspace associated to the eigenvalue -4 in the matrix -5 2 -4…

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Q: 2. Consider the quadratic form Q(r)=-6s²-10st-61². (i) Find the corresponding symmetric matrix. (ii)…

A: According to the guideline only three subpart can be answered. Please post other questions…