Orthogonally diagonalize the matrix -1 -2 1 2 3 | A = 1 -2 -1 1

Q: Determine whether the matrix is orthogonally diagonalizable.

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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: True or False: The following matrix is diagonalizable. 1 -0 -2

A: For the solution follow the next step.

Q: Diagonalize the matrix 1 0 -1 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix…

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Q: Determine the inverse matrix of matrix C. 2 3 C- -2 8]

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Q: (TRUE, FALSE) A matrix multiplied by its inverse is always equal to the identity matrix.

A: Introduction: Since it is mentioned that a matrix is being multiplied by its inverse, it can be…

Q: State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c) diagonal,…

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Q: Perform the matrix operation. (If not possible, enter IMPOSSIBLE in any cell of the matrix.) -4 -2 1…

A: Find out the matrix multiplication.

Q: Calculate the matrix P, the matrix D, det(P), and the matrix P! Is the matrix A2 diagonalizable?…

A: Solution:-

Q: matrix question

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Q: Determine the diagonal matrix. 1 -3 -2 0 0 0 4 (1 3 5)

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Q: 0 1 2 3 0 0 1 2 A = 0 0 0 1 12 - 0 0 0 0 A=[a] matrix can be expressed as

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Q: True or false? det(A) is a number, not a matrix.

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Q: Write the third column of the matrix as a linear combination of the first two columns, if possible.…

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Q: Explain this statement "The product AB of two matrices is defined only if the number of columns of A…

A: Let A is a mxn matrix  And N is a pxq matrix. While multiplying two matrices we multiply the rows of…

Q: snip

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Q: Perform the matrix operation. (If not possible, enter IMPOSSIBLE in any cell of the matrix.) 0 4 9 6…

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Q: A symmetric matrix A is positive def

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Q: Diagonalize the given matrix if possible: A = [1 2 0 -1

A: Our Aim is to diagonalize the matrix A=120-1

Q: 2 0 -1 2 0 0 1 1

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Q: Determine whether the matrix is symmetric, orthogonal, both, or neither.

A: Now transpose of A is, Hence A is a symmetric matrix.

Q: Find an LU-factorization of the matrix: show solutions. 1 1 a. 1 ⠀⠀ 2 2 2 3 2 5 b. 6 14

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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: What do 2 × 2 matrices represent graphically?

A: 2 × 2 matrices represent:

Q: State whether the matrix is diagonalizable or not. 0 0 7 0 O diagonalizable O not diagonalizable

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Q: True or false? det(A) is defined only for a square matrix A.

A: True/False det(A) is defined only for a square matrix A

Q: Orthogonally diagonalize the matrix 1 2 2 -2

A: Given,     122-2

Q: Determine whether the matrix is orthogonally diagonalizable.

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Q: Use the definition of Ax to write the vector equation as a matrix equation. - 6 8 - 1 - 9 5 3 X1 - 2…

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Q: Use the definition of Ax to write the vector equation as a matrix equation. 3 4 - 2 7 -3 + X2 - 9 5…

A: Given vector equation- x13-501+x24-3-99+x3-267-6=7198 To write the vector equation in matrix…

Q: True or False? Suppose that A is any n x m or n xn matrix, then the matrix A'A will be the transpose…

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Q: 으으 Evaluate the product by treating it as a linear combination of the columns of the matrix. The…

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Q: Let matrix A be 2 by 2 matrix and 1 A. 4 and 1 4 .2) 2 Then what is A=? ||

A: At first we will suppose a matrix A as 2x2 matrix and simplfy second condition by pre multiply by A…

Q: 4.) Determine matrix. 2-3 1 2 -2 6 X the dimension of the

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Q: 3. (30 points) Diagonalize the matrix A = 5 0 1 -1 05 0 0 0 0 4-3 0 -2 0-3 if possible.

A: 5000050000-30000-3

Q: Example: Add the components of a vector (u) to the principal diagonal of a matrix (C) that is the…

A: Example of Addition of component  of vector  u to principal diagonal of a matrix C that is sum of…

Q: Let -1 1 A = -1 1 -1 -3 3 Find an upper triangular matrix which is orthogonally similar to A.

A: An upper triangular matrix is a triangular matrix with all elements equal to below the main…

Q: Diagonalize the matrix if possible [ 0 1 1 2 1 2 3 3 2 ].

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Q: Matrix AA is transformed by a scalar to form matrix BB . A=[−1.5   3]       B=[3   −6] [4.25…

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Q: Find two 2 × 2 matrices such that ∣A∣ + ∣B∣ = ∣A + B∣.

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Q: Find the rank of matrix using Daussian elemination  method. A=[1 -1  2 , -3  3  -6 , 0  1  2]

A: NOTE: It is not "Daussian elemination  method", it is "Gaussian elemination  method".

Q: Q1. Q2 € Raxn. Q1 - Q2 (c) Show: orthogonal matrices

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Q: 2. Diagonalize the matrix: 1 0 -2 1 1 1 -1

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Q: Orthogonally diagonalize the matrix 1 -1 -2 A -1 2 -2 3

A: Given:   A = 1-1-2 -120 -203

Q: (0 8 1 1 4 -1

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Q: Use the definition of Ax to write the vector equation as a matrix equation. 4 - 3 + Z4 4 4 + Z2 + Z3…

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Q: а 3 2 Find the value of a that make the matrix A 1 2 3 3 1 2 - singular. a =

A: A matrix will be singular if value of its determinant is zero  => If A is singular then A=0

Q: 2. Orthogonally diagonalize the matrices. -4 4 1 5 (a) 5 1 (b) |-4 4 9

A: The given matrices are; a)  1 5       5 1 b).   7  -4  4        -4  5  0         4  0  9

Q: Define the properties of the inverse of a matrix?

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