'5. Consider the 5 × 5 symmetric matrix over R 10 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1. A = The rank is the number of linearly independent row (or column) vectors of A. (i) Find the rank of the matrix. Explain. (ii) Find the determinant and trace of the matrix. (iii) Find all eigenvalues of the matrix. (iv) Find one eigenvector. (v) Is the matrix positive semidefinite?

Q: 4. Consider w = and v =. (a) Write z = as a linear combination of w and v. (1 2 3 (b) Consider the…

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Q: 0 1 1. Consider the matrix A = -2 -3 Find (a) the characteristic equation of the matrix A (b) the…

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Q: Q2: (a) For given matrix A, find a 3 x 3 non-singular matrix P such that p-1AP is diagonal. A = |-3…

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Q: Find the coordinate matrix of x in R'" relative to the basis B'. B' = {(9, 0), (0, 7)}, x = (27, 28)

A: We have given basis B' and x, and we have to find corresponding coordinate matrix [x]B'.

Q: Assume the following matrix is given Be when x = I I I X 1000 000 1 00 1 0 where x is any non-zero R…

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Q: 21 Find the matrix that projects a vector from R onto the column space of the matrix 0 12 4

A: Consider the matrix A=120124. Columns of A are 102 and 214 . Clearly, they are linearly independent.

Q: -3 0 -1 0 -1 0 Find the eigenvalues and an orthonormal basis for each eigenspace. A₁ = -1 0 The…

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Q: 2 1 Let A = Show the details of two different methods [(1) using the adjoint and determinant, (2)…

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Q: = {[3] [7²]} and T = Let S and T be bases for R2, where S= and T=131-1 Find the change of base…

A: According to question,Given data,Let us assume s and T be bases for ℝ2,where,S = 13, -21T = 83, 47

Q: 4. Consider the matrix A= = 1 1 2 3 1 2 3 -4 -5 1 1 3-4 4 -5 8 Find the determinant of A via…

A: The solution is shown below- As per bartleby guidelines only first part is allowed to solve. Kindly…

Q: (Q13) Determine Eigen values and corresponding inverse of matrix for G if its determinant has a real…

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Q: By means of elementary row operations, find an invertible 3 × 3 matrix R such that RA= B where a+a…

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Q: For an NxN-dimensional matrix A, prove that a) the product of the eigenvalues is equal to the…

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Q: 3. Let 1 0 1 A = 3 1 2 4 1 3 (a) Find the determinant of A. (b) Is A invertible? Why or why not?

A: Given, For matrix invertible, .Where  is determinant of matrix.

Q: c) Find the eigenvalues for the given matrices. Hence, find the eigenvectors for each eigenvalue. [1…

A: As you ask too many question ,I only solved first one.

Q: Using the matrices. [1 0 1 R1 = 0 1 1 li o 1 [1 1 1] R2= 1 0 1 li 1 Find the matrix that represents…

A: Use the given matrices.

Q: Find the Cofactor Matrix of Matrix B= 3 7 -2 -11 5 8 6 9 -2 4 8 -2 12 20 6

A: We need to find cofactor.

Q: 1 if k = i and l = j if k = j and l = i if k = l but k # i, j 1 (Si3)ke = 1 otherwise.

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Q: A = 60- -5 1 0 0 9 2 M33 = A33 = 32

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Q: 3. True or False (and justify): A matrix that has a left inverse must be wide. 4. Prove that for any…

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Q: If B is invertible matrix, then (5BT) = (A) 금BT (B) 5 (B-1)" (C) 5 (B")- (D) B-1 (E) (B-1)"

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Q: (4) Let B be the matrix 1 1 3 В - 3 4 -3 -6 (4a) Find the inverse matrix B¬1. (4b) Given the…

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