Show that the product of two orthogonal matrices is orthogonal.

Q: Determine whether the matrix is orthogonally diagonalizable.

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Q: Find two different 2x2 matrices A and B such that AB = BA. %3D --. .. (Use a comma to separate…

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Q: Determine if the matrix is diagonalizable

A: Given matrix, A=200-121101 we know that, if a matrix A is an n×n matrix, then it must have n…

Q: TRUE/FALSE The product of two elementary matrices is an elementary matrix.

A: False.  For example , the matrices are elementary matrices as they are obtained from I2 by single…

Q: Prove that diagonal matrices are symmetric matrices.

A: Given: diagonal matrices are symmetric matrices

Q: What is the closure property of multiplication? (applied to matrices and scalars)

A: Closure property of multiplication: (applied to matrices and scalars) Multiplication of any two…

Q: Show that the product of two orthogonal matrices is also an orthogonal matrix. Is the product of two…

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Q: Find inverse of matrix 1  2  3 0  4  5 0  0  6 Using augmented matrix  Show work

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Q: Show that the inverse of an invertible lower triangular matrix is lower triangular

A: Given : The matrix A is an invertible lower triangular matrix Then we have to show that A-1 is…

Q: Show that the inverse matrix of an upper (or lower) triangular matrix is ​​also triangular top (or…

A: prove is given below...

Q: Is every diagonal matrix a scalar matrix? Explain.

A: We have to explain that every diagonal matrix a scalar matrix. We know that diagonal matrices are…

Q: Which of these matrices are lower triangular matrices?

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Q: Determine all 2x2 matrices such that A? = I,: A- (: :) 0. b

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Q: Is the matrix diagonalizable? If yes, find diagonal matrix D and regular matrix P such that AP = PD.…

A: Yes, Given Matrix is diagnolizable.

Q: State whether the matrix is diagonalizable or not. [::] diagonalizable O not diagonalizable

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Q: Determine which of the matrices in are orthogo-nal. If orthogonal, find the inverse. -4/5 3/5 3/5…

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Q: () Write the statement of Cayley-Hamilton theorem for square matrices.

A: Cayley-Hamilton statement

Q: Find the change of basis matrix from B2 to B1. -4 B1 = , B2 B2 = 2

A: The change of basis matrix C from B2 to B1( or from the basis B2 to the basis B1 ): β1=-142,231  and…

Q: 2 0 -1 2 0 0 1 1

A:

Q: Find an orthogonal matrix whose first row is (1/3,2/3,2/3)

A: The rows of an orthogonal matrix forms an orthonormal basis. Therefore, consider the extended basis,

Q: Show that the inverse of a nonsingular lower triangular matrix is lower triangular.

A: We have to prove that inverse of a nonsingular lower triangular matrix is lower triangular.

Q: Determine the inverse matrix of matrix C.

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Q: Is the product of two elementary matrices always elementary? Explain.

A: To check product of two elementary matrices will be elementary or not.

Q: Prove that the inverse of an orthogonal matrix is orthogonal.

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Q: Write a second degree equation matrix and prove that it is in vector space?

A: To show: An example of a second-degree equation matrix which is in vector space.

Q: Determine which of the matrices in are orthogo-nal. If orthogonal, find the inverse. 2/3 1/3 -2/3…

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Q: Explain the Main diagonal within a matrix ?

A: The main diagonal within a matrix consists of those elements which lie on the diagonal that runs…

Q: Determine whether the matrix is orthogonally diagonalizable.

A:

Q: What is the multiplicative identity property? (applied to matrices and scalars)

A: Given: multiplicative identity property

Q: Define the term Scalar multiplication of matrices?

A: Concept: A rectangular array of numbers (or other mathematical objects) for those the operations…

Q: Determine which of the matrices in are orthogo-nal. If orthogonal, find the inverse. 2/3 1/3] 1/3…

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Q: Let r1, .. r,be vectors in R", and let Q be an m xn matrix. Write the matrix Qr, Qr, as a product of…

A: Given:Let r1.......rp be vectors in ℝnLet Q be an m×n matrix Qr1.......QrpR=r1.......rpQ=Q…

Q: Determine if the matrix is diagonalizable.

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Q: Is it true that Every identity matrix is a diagonal matrix? explain a reason?

A: A square matrix B=[bij] of order n is a diagonal matrix , if all its non-diagonal elements are 0,…

Q: Explain why the row vectors of a 4 × 3 matrix form a linearly dependent set. (Assume all matrix…

A: Given: The Matrix is 4 * 3 matrix

Q: Describe all 1 by 1 and 2 by 2 Hermitian matrices and unitary matrices.

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Q: State whether the matrix is diagonalizable or not. 0 6 0 0 O diagonalizable O not diagonalizable

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Q: Show that a triangular matrix is normal if it is diagonal

A: Given: A triangular matrix is normal.if it is diagonal

Q: What are the Symmetric Matrices?

A: we know that if transpose of a matrix is equal to itself, then that matrix is said to be symmetric…

Q: Find the LU composition of 1 | - matrix A =

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Q: Find the change of basis matrix from B2 to B1. B2

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Q: Find the inverse of the Attached matrices.

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Q: Prove that diagonally dominated matrices are always invertible.

A: Suppose A be a n×n diagonally dominated matrix. Therefore: aii>∑i≠jaij. Suppose A is not…

Q: The i-th column vector of an AB matrix product can be calculated by multiplying A by the i-th B…

A: True Because take A=a11a12a21a22 and B=b11b12b21b22 Then the product of AB is,…

Q: V3 Express 1 as a product of elementary matrices.

A: Solve by matrices

Q: Which of the following matricesare diagonalizable?

A: Diagonalize 141-2:  4-111200-31515-1545Diagonalize 1-2-21:  -1111300-1-12121212Diagonalize…

Q: Determine which of the matrices in are orthogo-nal. If orthogonal, find the inverse.

A:

Q: Find the inverse of the elementary matrix.

A: Given matrix, A=0110