6. Assume that a 3 × 3 matrix A has three eigenvalues A₁, A2 and λ3. If A₁ = A₂ = 2, A3 = 6 and the trace of A is 5 + x. Then x is equal to (a) 5 (b) 4; (c) 3; (d) 2; (e) None of these

Q: [584] 3. The eigenvalues of the matrix A= 8 5 4 are A₁ = A₂=-3, A3= 15. 4 Find the corresponding…

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Q: Suppose that A is a 3 x 3 matrix with the following properties: 4 -5 is an eigenvector for A…

A: Given that A is a 3×3 matrix with the following properties :  u = 4-5-1 is an eigenvector for A…

Q: Suppose that a 5 x 5 matrix A has eigenvalues > −3,-, 1,2,4. Compute det(A). ==

A: Suppose that a 5×5 matrix A has eigenvalues λ=-3, 12, 1, 2, 4. To compute detA.

Q: Prove the following for any two matrices A and B of order ( 2 x 2). (A + B)² = A² + AB + BA + B² %3D…

A: 1. a. We need to prove the following for any two matrices A and B of order 2x2 A+B2=A2+AB+BA+B2

Q: The trace (sum of entries on the main diagonal) of a matrix is equal to the sum of the eigenvalues…

A: Given: Trace of 2×2 matrix (trA)=14 determinant of 2×2 detA=45 Now, Let λ1 and λ2 be eigen values of…

Q: If u1= then A(01+02) = and A(-201) = and 2 = Gl are eigenvectors of a matrix A corresponding to the…

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Q: 3. For the set of simultaneous equations: a. Form the augmented coefficient matrix b. Solve the…

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Q: Suppose that the trace of a 2 x 2 matrix A is tr(A) = = 0, and the determinant is det(A) = -49. Find…

A: Given that the trace of a 2 * 2 matrix A is tr(A) = 0 and the determinant is det(A) = -49. Find the…

Q: 4. Find the eigenvalues of the matrix B = 1 3

A: The eigen values of a matrix A is the roots of the characteristic polynomial of the matrix. The…

Q: Suppose A is a 2 × 2 real matrix with an eigenvalue λ = 3 + 4i and corresponding eigenvector * = [-…

A: We have to determine the fundamental set of solutions for x' = Ax for given eigen value and…

Q: Suppose matrix A is symmetric and has eigenvalues X₁ = 7 and X₂ = 2. The corresponding eigenvectors…

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Q: 1. Show that the matrix 2 1 A = 1 2 -1 -1 is positive definite.

A: Given :- a matrix A  We need to show that a matrix is positive definite. We know that , A symmetric…

Q: Write whether the following statements are true or false with the whole word. (a) (5) If M is a…

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Q: Given a matrix A = a b and denoting its eigenvalues by 2₁ and 22 (note that these can be the same…

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Q: 3. An n x n matrix A is called nilpotent if there is some k ≥ 0 such that Ak = 0 (i.e., Ak = (n x n)…

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Q: (c) Find f(A), where f(t) = tª – 4t3 + 3t – 7.

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Q: Suppose A is a real symmetric matrix whose eigenvalues are A₁ = 1, A2 3, and X3 ei = Find A. A = = 9…

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Q: |A| = 24, f Adj A =

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Q: Suppose that the trace of a 2 x 2 matrix A is tr(A) = -14, and the determinant is det(A) smaller…

A: Let A be a square matrix,  then The trace of A is the sum of eigenvalues and The determinant of A is…

Q: 2. Suppose A is a square matrix and A² = [0] (the zero matrix). (a) Explain why X = 0 is the only…

A: A is a square matrix and A2=0(the zero matrix)

Q: Find the 2x2 matrix B given its eigenvalues = 1 and 2=3 and the corresponding eigenvectors v₁=(-1,1)…

A: For a matrix B ,if λ is an eigen value and  X is the corresponding eigen vector then    BX = λX

Q: ne ei genvalues o

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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…

Q: If A is an n × n matrix with eigenvalue 0, then dim (null(A)) > 0.

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Q: 8. Let A and B are square matrices of the same order and let S non-singular matrix and A similar to…

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Q: 3 0 0 -2 7 2. Find h in the matrix A= such that the eigenspace for A=7 is one- -1 0 4 -6 5 7…

A: Here, the matrix is A=3000-27000h-104-657 and the eigenvalue of the matrix is λ=7.

Q: If matrix A is square of size n x n with a rank equal to 2 and n > 2. The rank of a matrix is equal…

A: Given that, matrix A is square of size n×n with a rank equal to 2 and n>2. the rank of a matrix…