A nxn matrix that satisfies AT = A-! is called an orthegonal matrix. Find the cleterminant of Such a matrix CPlease show both possiloilities).

Q: FIND THE FUNDAMENTAL MATRIX AS WELL AS THE FUND AMENTAR MATRIX ø (6)= I %3D SATISEYING x' = 2 -5 -2

A: Fundamental matrix is formed with linearly independent solution sets of the system. These linearly…

Q: (3) Show that the system of quaternions can be represented as a system of real matrices of size 4 x…

A: Let h, j, k denote the imaginary units of algebra of Quaternions. Then the typical quaternion is in…

Q: Define bidiagonal matrix.

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Q: must be a non-invertible matrix.

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Q: Without using any theorem, show that there is not a Hadamard matrix of order 5.

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Q: Find the basis of row space of the matrix A given in the attached image . Please answer quickly .

A: A=1231337638-2-5-30326024351312R2⇒R2-3R1, R3⇒R3+2R1, R4⇒R4-2R1,…

Q: Using only 0's and l's, list all possible 2 × 2 matrices in row canonical fom.

A: Row canonical matrix All zero rows, if any, are at the bottom of the matrix. Each leading non zero…

Q: If A * I = A, and A is a 3x5 matrix, what are the dimensions of I? Show complete solution as proof.

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Q: matrix with eig satisfies

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Q: Let A be an 8 × 5 matrix of rank 3, and let b be anonzero vector in N(AT ). Show that the system Ax…

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Q: Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.

A: Consider a square matrix A=000123456 and B=140250360 Here, all the elements of first row of the…

Q: The maximum value of the determinant among all 2×2 real symmetric matrices with trace 16 is

A: But they cannot be both negative as a+d=16 And the value of ad is maximum  a=8, b=8 Therefore

Q: Let Q be a matrix with orthonormal columns, then QQT = 1. :Select one True False

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Q: Find an LU-factorization of the matrix A such that A = LU. %3D 6 4 -2 1 -2 3 2. -2

A: Explanation of the answer is as follows

Q: Give an example of a 3x3 non triangular matrix with with eigenvaluse 2,3,-2

A: Give an example of a 3x3 non triangular matrix with with eigenvaluse 2,3,-2

Q: What does it mean that matrix A is orthonormal? What does it mean that matrix A is positive…

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Q: Find a sequence of elementary matrices whose product is the given nonsingular matrix.

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Q: Suppose A and B are nxn matrix and P is an invertible nxn matrix such that A = P-BP (a) Show that A™…

A: We will use Diagonalization  and proof of first part to find power of matrix

Q: If Q is an orthogonal matrix, prove that any matrix obtained by rearranging the rows of Q is also…

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Q: Let I be the rdentity of nxn. Please Compute 3. matrix the matrix funct ions CosT I (i²=-1)

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Q: why cant we just multiply the 1/det(A) with the transpose of matrix like indicated in the red…

A: I am attaching image so that you understand each and every step.

Q: If there is conformability what are the dimensions of the product matrix?

A: let's matrix A and matrix B has dimension as  m×n and n×p respectively then dimension of matrix…

Q: Let A be an m x n matrix with rank m and B be ann x p matrix with rank n. Determine the rank of AB.…

A: to find the rank of AB.

Q: Find Jordan form of this matrix

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Q: 1. Verify whether the two given matrices are similar. To justify yo perform suitable calculations or…

A: Note: Since you have asked multiple questions, but as per Bartleby guidelines we will solve the…

Q: Suppose there is diagonal matrix D that is congrutent to a symmetrix matrix A. Can the eigen values…

A: Given that A is symmetric matrix And suppose there is diagonal matrix D that is congruent to a…

Q: Show that the matrix below does not have an LU-factorization.

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Q: Find all aclh for which the matrix A = [at3 2 b non-singular.

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Q: The diagonal elements of a 3x3 matrix are 2, 1, -3 are respectively. If two of its eigen values are…

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Q: suppose A be any Hew of have symmetric matoir order and this matrix 4x4 rank of 3 the caleulata the…

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Q: Suppose a 3x8 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…

A: Ans: Given a 3×8 matrix has a rank 3. We want to find the dimension of the null space, dimension of…

Q: Find an upper triangular matrix that satisfies 18 -8 0

A: Given  A3 = 1180-8 It is an upper triangular matrix , hence its diagonal are the eigen values of the…

Q: Let X and Y be symmetric matrices both size 15x15. Decide if Z = XT(X+Y) is a symmetric matrix too.…

A: Given, X & Y are symmetric matrices. So, XT = X and, YT = Y   Given, Z = XT(X+Y) So, ZT =…

Q: How do you determine the sensitivity for each non zero parameter in this leslie matrix model

A: To determine sensitivity of 2x2 matrix. Let, the 2x2 matrix be a b c d Here,  True positive…

Q: Give am example of a 6×6 positive definite banded matrix A with band width 5 (or semiband width 2)…

A: Example of 6x6 positive definite banded matrix with band width 5  A=…

Q: If the sum of dimensions of all eigenspaces for nxn matrix A is less than n then any vector from Rn…

A: Let X1, X2, · · · , Xk be eigenvectors correspondingto distinct eigenvalues λ1, λ2, · · · , λk of…

Q: 2. for the augmanted matrix

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Q: Find the greatest value of A that make the matrix 2 – 9 – A - A singular. – 6 -2 – X.

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Q: find the given matrix is Identity matrix if not find determinant of the matrix without ing NumPy…

A: For Identity matrix, the diagonal element of the matrix should be 1 so its determinant always 1 and…

Q: Find the 3x3 homogeneous matrix for 2D-reflection across a line that goes through (B, C) and makes…

A: As per the question we have to to find the transformation matrix which reflects any point on 2d…

Q: Show that Foranyeigen value Tofthe nonsingu lar matrix A with any natural norm Then

A: Given, Eigenvalue λ of non singular matrix A To prove : 1∥A-1∥≤λ≤∥A∥

Q: Find an SVD of the indicated matrix. (Enter each matrix in the form [[row 1], [row 2], ...], where…

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Q: Construct a nonzero 2 × 2 matrix that is invertible but not diagonalizable.

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Q: If A and B are diagonalizable nxn matrices and have the same eigenvalues with same multiplicites,…

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Q: Find the SVD and then the Rank-1 approximation of attached matrix A.

A: Solution is here

Q: 3) Develop matrix form of the quadratic spline polynorhials for these data po: (1, 1), (2, 3), (3,…

A: Given: 1,1,2,3,3,5,4,2 n=4

Q: (a) Determine a lower triangular matrix L with 1s on its diagonal and D a diagonal matrix with…

A: a The given matrix A=2-10-12-10-12consider a lower triangular matrix L and diagonal matrix D…

Q: Give at least 3 examples of each type of matrix with solution: 1.Orthogonal Matrix 2.Involutory…

A: 1. Orthogonal matrix : A square matrix A is called orthogonal if AAT = I = AT A. Example 1:…