if A1 = 3+3i and A2= 3- 3i are two eigenvalues of 2 2 matrix A then the determinant of A equal Select one: a. 18 b. 14 С. 9 d. 3

Q: Given two m ×m matrix X and Y , where XY = Y X. Suppose the eigenvalues of X are mutually different…

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Q: The matrix has three distinct real eigenvalues if and only if <k< A = -1 -8 k 0 0 0

A: Consider the given matrix, A=-1-10-80-1k00 The charactertics equation of the matrix will be A-λI=0,…

Q: Suppose that a 4 x 4 matrix A has eigenvalues A₁ = 1, A2=-7, A3-9, and A4-9. Use the following…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Let the trace and determinant of a 2 x 2 square matrix A be Tr (A) = -1 and det (A) = -2 respec-…

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Q: if A1= 3+3i and X2= 3- 3i are two eigenvalues of 2*2 matrix A then the determinant of A equal Select…

A: Since, product of eigenvalues is equal to determinant So

Q: 17 7 Find the eigenvectors of the matrix - 42 – 18 The eigenvectors corresponding with A1 = 3, A2 =…

A: Given matrix is A=177-42-18A-λI=17-λ7-42-18-λ The eigen values of matrix A are λ1=3, λ2=-4 Let x1x2…

Q: Given two m ×m matrix X and Y , where XY = Y X. Suppose the eigenvalues of X are mutually different…

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Q: For which value of k does the matrix -7 k A = 9 7 have one real eigenvalue of multiplicity 2? k ||…

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Q: Suppose A SAS1, then the eigenvector matrix of A + 41 is %3D O a S+ 41 Ob. S OcS+I d. S-41

A: We will find the diagonal matrix corresponding to the matrix, A+4I

Q: If A is a 3 x 3 matrix with eigenvalues 2,-2,1. Let 8 = A - 3A2 Then det(B) = -160 Select one: True…

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Q: If A is a 4 x 4 matrix such that 3 is the only eigenvalue of A, then the characteristic polynomial…

A: Eigen values are the roots of the characteristics equation. If n×n is the matrix than there are n…

Q: The eigenvectors of the matrix A .4 . are written in the form v_1 and v_2 ?What is a + b A - ( ) ()…

A: Given: A matrix A=1202 with the eigenvectors v1=1a, v2=1b.

Q: If 1 4 and v2 are eigenvectors of a matrix A corresponding to the eigenvalues A1 -4 and X2 = 1,…

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Q: If ö, = and vz = are eigenvectors of a matrix A corresponding to the eigenvalues A = 5 and A2 = 1,…

A: Topic:- eigen value and vector

Q: Suppose that a 4 x 4 matrix A has eigenvalues A, = 1, d2 = - 6, A3 = 8, and 14 = - 8. Use the…

A: The eigen values of matrix A can be found by solving the equation detλI-A=0. For 4×4 matrix, maximum…

Q: Given the following matrix 4 4 -3 Find its two eigenvectors. and H2 A and H2 B) H, = 9 4 and 2 4 4…

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Q: Suppose that the matrix A has the following eigenvalues and eigenvectors: A = 2+ 3i with ở = -5+ and…

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Q: The 3 x 3 matrix B is known to to have eigenvalues 0, 1, and 2. Is this information enough to…

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Q: Suppose that a 4 x 4 matrix A has eigenvalues g = 1, 12 = - 2, 13 = 3, and A4 = - 3. Use the…

A: Properties based on eigen values: Product of eigen values is equal to determinant of corresponding…

Q: If vj = and 02 are eigenvectors of a matrix A corresponding to the eigenvalues 11 = 4 and 2 = -1,…

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Q: Let M be a 2 x 2 matrix with eigenvalues 11 = 0.9, 12 = -0.25 with corresponding eigenvectors V1 = ,…

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Q: Suppose that A is 2x2 matrix with eigenvectors V, = which correspond to A,=3, 1,-2 respectively.…

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Q: 9 The matrix has eigenvalues d1 = 3 and A2 = 5. Find the %3D -4 -1 corresponding eigenvectors. and…

A: Given that  The matrix  And corresponding Eigen values are 3 and 5  And to find the corresponding…

Q: For which value of k does the matrix -3 k A 4 4 have one real eigenvalue of multiplicity 2? k =

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Q: Suppose A is indefinite matrix and one of the eigen values is 1, then O a. a = -1 O b.a = 1 Oca = 2…

A: given,        eigen values=1                        then, α=?

Q: The matrix has three distinct real eigenvalues if and only if 0 <k < 427 1 1 07 A 0 1 1 k 0 0

A: Given matrix A=110011k00 The matrix has 3 distinct real eigen values. We already have characteristic…

Q: Given that v 3 and v2 are eigenvectors of the matrix 15 48 A -4 –13

A: To find The corresponding eigenvalues of the given matrix A.

Q: A matrix A has the following eigenpairs. Complete the eigenpairs. 5 – 7i Ex: 3+ 7i d = Ex: 3+ 7i X =…

A: See the attachment

Q: The matrix has three distinct real eigenvalues if and only if <k < 1 07 4 A = 4 4 1 k 00 A4

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Q: For which value of k does the matrix A=[2   k]     [−4 5]   have one real eigenvalue of…

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Q: If A is n x n matrix and A² = aA and the eigenvalues of A are ±4j then the value of a is a. 2 b.-2…

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Q: Suppose A is a 3×3 symmetric matrix such that [x_y_1]4|\y=xy-1. X If p is the number of positive…

A: My solution is correct,  so request you to check your options  for q please.

Q: For matrices A and B with B invertible AB and BA have the same eigenvalues.

A: soln:If A &amp; B are two square matrices of order n then, AB &amp; BA have same eigen values.Let A…

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

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Q: If A is a 3x3 matrix with eigenvalues 1 and​ 2, which option is impossible for diagonal matrix​…

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Q: nd the matrix A that has the given eigenvalues and corresponding eiger 24 = 1= {},2 = 3= {} 11 -4 14…

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Q: [3 For A = find the eigenvalues 1,andlz and the orthonormal eigenvectors v,and vz. 13 Form the…

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Q: If A is an eigenvalue of the matrix A, then X must be an eigenvalue of which of the following…

A: Given that λ is an eigenvalue of matrix A and we know that for any vector x, we have Ax=λx. We have…

Q: If A is a 4 x 4 matrix such that 3 is the only eigenvalue of A, then the characteristic polyn of A…

A: Solution of the problem as follows

Q: Let the trace and determinant of a 2 x 2 square matrix A be Tr (A) = 5 and det (A) = 6 respectively.…

A: We have to find the Eigen values.

Q: [:] If vị and v2 = -1 2 are eigenvectors of a matrix A corresponding to the eigenvalues A1 = –4 and…

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Q: The matrix A: = has two distinct real eigenvalues if and only if k> 25

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Q: 1.4: An eigenvector for value of λ = -2 for the matrix a) H b) © H H e) None of the above is

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Q: Suppose that a 4 x 4 matrix A has eigenvalues A, = 1, A2 = - 3, A3 = 5, and A4 = - 5. Use the…

A: Given: λ1=1, λ2=-3, λ3=5 &amp; λ4=-5 detλI-A=λn+c1λn-1+⋯+cn For n=4, detλI-A=λ4+c1λ3+c2λ2+c3λ+c4

Q: Given that 1, 2 and O are eigenvalues of matrix S. The following number is a possible value of x…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: If A and B are two row equivalent matrices, do they necessarily have the same eigenvalues? Either…

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Q: - If o1 1 and v2 -2 are eigenvectors of a matrix A corresponding to the eigenvalues d1 1 and A, =…

A: Definition of Eigenvector, Eigenvalue:   Avi = λivi    for all i, in this case, i = 1, 2

Q: Linear algebra problem

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Q: Solve the following matrix system by using variation of parameters: dx *- ( )) 1 x + 5e-t %3D dt 4…

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Q: if A, = 3+3i and X= 3- 3i are two eigenvalues of 2*2 matrix A then the determinant of A equal Select…

A: We have to find determinant