One of the properties of eigenvalues is the sum of all the eigenvalues of the matrix is equal to the trace of the matrix. Given that a matrix A is defined as follows: (c) -2 -4 2) A = (-2 2 1 5. 4 2 (i) The eigenvalues of A are 11 = -5, 12 = 3 and 13. Using the property mentioned above, calculate the third eigenvalue, 13. (ii) Find the eigenvector corresponding to l1 = -5.

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Q: a) Determine the eigenvalues and eigenvectors of the following matrix. 3 -2 1 2 -4 3 l16 -4 1

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A: Eigenspace and eigenvalues

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Q: For which value of k does the matrix have one real eigenvalue of multiplicity 2? k= -2 A = [ 2₂4]

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Q: A = -53 -70 35 45

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Q: (d) cation. [11] =2 Write out eigendecomposition of A and verify it with the matrix multipli- m,

A: Eigenvalue decomposition:A=QDQ−1Where the columns of Q are the orthonormal eigenvectors and the…

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: the matrix, list the real eigenvalues, repeated according to their multiplicities. 9 -3 0 4 3 0 4 0…

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A: our objective is to find the eigen value.

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A: We will find out the required value.

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A: To find the eigenvalues of the given matrix if we solve the characteristic equation M-Iλ=0

Q: 8. The eigenvalues of a matrix A are 7 and –1.

A: 8). Given, the eigenvalues of a matrix A are 7 and -1 with corresponding     eigenvectors are 12…

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Q: If the eigenvalues of a 3×3 matrix A is 1, −2 and 20, what are the eigenvalues of A-1?

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Q: For the matrix, list the real eigenvalues, repeated according to their multiplicities. 3 -20 4 0 21…

A: if the given matrix is A then eigen value are:-  det(A-lembda i)=0

Q: Determine the eigenvalues and eigenvectors of the following matrix: 6 [39]

A: Use the given matrix.

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Q: Find the rank and nullity of the given matrix. 3 1 3 The rank is The nullity is Check Answer

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Q: こ Find all eigenvectors of the the matrix A= 4 1 2 3 (a) ; (d) ; (b) ; (c) ; C O b

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Q: Find all eigenvalues and eigenspaces (bases) for the 3 by 3 matrix [each parentheses O) is a column]…

A: Use eigen value concept