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Q: If (AB)" = and A = find the matrix B. %3D

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Q: Determine whether the matrix is orthogonally diagonalizable.

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Q: Determine whether the matrix is symmetric, skew-symmetric, or neither. A square matrix is called…

A: Here we have to determine whether the matrix is symmetric, skew-symmetric or neither.

Q: Determine whether the matrix is elementary. If it is, state the elementary row operation used to…

A: A square matrix of order n is elementary matrix if it is obtained from the identity matrix In by a…

Q: Let A be an nxn matrix and B= A+ I, where / is the identity matrix, then it is possible for A and B…

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Q: Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u. 7 3. Let y =…

A: Find the orthogonal projection of the vector y on u., which will give the y^. Then to find z,…

Q: Determine whether the given matrix is diagonalizable 3 1 A = 0 1 3

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

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

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Q: Determine whether the matrix is symmetric, skew-symmetric, or neither. A square matrix is…

A: Given matrix is

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

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Q: Find the detemination of matrix:- B 1 2

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Q: Determine if the matrix is nonsingular. Explain. [1 3 21 1 4 l1 -7 21

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

A: Solution:-

Q: Find an orthogonal matrix Q and a diagonal matrix D

A: Follow the procedure given below.

Q: The 2 ´ 2 identity matrix is:

A: To find:

Q: Determine whether the matrix is elementary. If it is, state the elementary row operation used to…

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

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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: What is the name of the matrix, Sij?

A: Sij is called as similarity matrix.

Q: Show that if A is a symmetric matrix, then Ak , k = 2, 3,... , is symmetric.

A: Given that, A is a symmetric matrix. Then we get, A^T = A; where A^T is the transpose of matrix A We…

Q: Identify that the given matrix is Diagonalisable or not: -2 = | -2 6

A: A matrix is said to be diagonalizable if it is similar to a diagonal matrix. Also, if a matrix has…

Q: Identify that the given matrix is Diagonalisable or not: -2 A = 2 6 -1 1 5.

A: It is diagonalisable

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

A: To determine whether the matrix is symmetric, orthogonal, both, or neither.

Q: A symmetric matrix A is positive def

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Q: (b). Find out the similar matrix of given matrix:

A: Similar Matrices: Ant two matrices A and B are said to be similar if there exists an invertible…

Q: Determine whether the matrix is symmetric, skew-symmetric, or neither. A square matrix is…

A:

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

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

Q: Determine whether the matrix is symmetric.

A: Now the transpose of this matrix is,

Q: Decide whether the matrix -7 1 4 A = -12 1 8 -10 1 7, is diagonalizable over R. If it is,…

A: -714-1218-1017

Q: Calculate the rank of each matrix by converting it into canonical form…

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Q: Find the two by two matrix A such that A -

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Q: Find the inverse matrix of A

A: We are given :A=13-201-6001 ⇒A=1(1-0)-3(0-0)-2(0-0)=1≠0 ⇒A is Invertible. Formula for Finding A-1:…

Q: (a) Find the matrix A so that AB=C, where а, а, а, B= b, b, b, & C= b, b, b, a, az az (2 rows are…

A: Given B=a1a2a3b1b2b3c1c2c3 now using row operation R1↔R3 ~c1c2c3b1b2b3a1a2a3

Q: Let A be an nxn matrix and B = A+1, where I is the identity matrix, then it is possible for A and B…

A: Given A be an n×n matrix nd B=A+I where I is the identity matrix , then it is possible for A and B…

Q: If a matrix A has 2 linearly independent columns, then dimRow(A)=2. True O False

A: Please find the solution in the below step

Q: Write a 4  6 matrix with distinct non-positive entries and find its transpose.

A: The objective is to write a 4×6 matrix with distinct non-positive entries and find its transpose .

Q: L- matrix and U

A: The objective of the question is determine the L- and U- matrix.

Q: Use the of a the inverse Possible. w/or O matrix capabilities calculator to find the matrix, of 2…

A: Find the inverse of the given matrix.

Q: Determine whether the matrix is symmetric. -1 4 4 1 O symmetric O not symmetric

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Q: 3 (i);- 2

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

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

Q: Solve the Matrix Equation XAB-BAX=X with A,B,X are nxn matrix with A,X are invetribles.

A: The given matrix equation is, XAB-BAX=X where A, B and X are n×n matrices with A and X invertible.

Q: Consider the matrix A =

A: Given, the matrix                       A=420040004

Q: 1- the rank of the matrix A.

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Q: Determine whether the matrix is in echelon form, reduced echelon form, or neither. Select one:…

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Q: Find a Cholesky factorization of the following matrix.

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Q: Give an example of a nonzero 3 x 3 diagonal matrix A. A =

A: Diagonal Matrix: In linear algebra, a diagonal matrix is a matrix in which the entries outside the…