Find a 2 x 2 orthogonal matrix P whose first row is a multiple of (a) (3,–4), (b) (1,2).

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

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Q: Find an SVD of the matrix. -6 5 A = 0 6

A: We have to general eigenvalue and eigenvectors to find Singular Value Decomposition of matrix A We…

Q: Give an example of a 4 x 4 matrix that is symmetric, has with the (2,4)-entry equal to -5, and has…

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Q: Find the LU factorization of the matrix A, where 3 -5 2 3 2 -2 A = -1 -6 1 -1 -4 1 2 1 2.

A: We know that A = L U where L is the lower triangular matrix and U is the upper triangular matrix.

Q: Express the invertible matrix (1 2 1 10 1 1 2) 1 as a product of elementary matrices.

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Q: Find x such that the matrix is singular. 4 A = -2 -6

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Q: Explain why the matrix A + C does not exist.

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Q: Find a 2 x 1 matrix x with entries not all zero such that 2 Ax = 3x, where A = 1 2

A: Given matrix is A=2   11   2 and condition is Ax=3x

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

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Q: Factorize the matrix into LU decomposition. [0 5 41 A = 5 1 2 1 2 3.

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Q: Give an example of a 3 x 3 lower triangular matrix A that is not diagonal. A =

A: We write the 3x3 lower triangular matrix which is not diagonal

Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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Q: Find inverse of matrix A by using elementary row operations where 1 0 - 2 A = 3 1 -2

A: Consider the provided matrix, A=10-2   31-2   -5-19 Find the inverse of the matrix. First, we write…

Q: .

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Q: Disprove that the rank of a matrix is equal to the number of nonzero rows.

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Q: -2 1 2 1

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Q: determine the general solution to the linear system x′= Ax for the given matrix A.

A: To Determine: The general solution of the linear system x'=Ax, whereA=-616-5 Concept: To Solve…

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: Find the characteristics equation of the matrix [1 2 A -2 -1 01 and hence find A-.

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Q: Show that any nX n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

A: To show that any n x n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

Q: Find a 2 x 2 orthogonal matrix P whose first row is a multiple of (а) (3, —4), (b) (1,2).

A: Find a 2x2 orthogonal matrix P whose first row is a multiple of(a) (3,-4) (b) (1,2)

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 4 - 4 2 - 8 2 - 1 A = 10 8…

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Q: Find a 2 x 2 matrix B so that B2 = A, where

A: Given matrix A=-7-16817 To find matrix B such that B2=A.

Q: ГО 5 4 5 1 2 2 3] A = [1

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Q: Give an example of a 3 x 3 upper triangular matrix A that is not diagonal. A =

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Q: Find x such that the matrix is singular. A- -2

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Q: A = 2 - 4 4 -2 6-9 7 -3 -1 -10 18 -7

A: Sol

Q: Find a QR-decomposition of the matrix -1 1 1 -1 0 1

A: Here,             . Now, we will be finding the QR decomposition of the above matrix A.

Q: The matrix X1 X = is called a vector.

A: We have to find

Q: Find the symmetric matrix that corresponds to the quadratic form q(x, y, z) = 3x² + 4æy – y² + 8xz

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Q: If A = 1 y and the transpose of the matrix is equal to the inverse of the matrix then y =

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Q: Find the augmented matrices of th e linear systems x +5y = -1 , -x + y = -5 ,2x + 4y = 4

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Q: Find the augmented matrices of th e linear systems x - y = 0 ,2x+y=3

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Q: Find x such that the matrix is singular.

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Q: Supply a third column so that the matrix will be orthogonal: V5/5 2/3 2/5/5 -1/3 2/3

A: 1. A matrix Q of order n×n is said to be an orthogonal matrix if, QTQ=QQT=In where QTrepresents…

Q: Find a (2x2) singular matrix A that maps (2, 2) into (1, 2).

A: Here in this question find a 2×2 matrix that maps (2,2)  into (1,2). Here i attached solution of…

Q: Supply a third column so that the matrix will be orthogonal: V5/5 2/3 2/5/5 -1/3 0 2/3

A: The given question is related with orthogonal matrix. Given the matrix ,…

Q: 3 (i);- 2

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Q: Find the inverse of the matrix and verify that A-!A = AA1- 1. 4--10 A 3D 2. 8. A-1 Show My Work…

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Q: Find an LU factorization for the matrix: 1 2 1 2 1 2 -2 0 1

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Q: Find 2x2 invertible matrices A and B such that A + B not equal to 0 and A + B is not invertible.

A: Wee need to find matrix A and B and do their addition and find invertible

Q: A is a 3 x 3 matrix with two pivot positions.

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Q: Find the LU factorization of the matrix A, where 3 -5 2 -2 A = -1 -6 1 -4 1 2 1 2. 2.

A: Given matrix is A=−23−5232−22−1−61−1−4121. We have to find the LU-factorization of the matrix A. By…

Q: Find 4x4 nilpotent matrices of indices 2, 3,  and 4

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Q: Find a 3 x 3 orthogonal matrix P whose first two rows are multiples of (а) (1,2,3) and (0, -2,3),…

A: To find the matrix

Q: Reduce the quadratic form 3x2+5y2+3z2-2yz+2zx-2xy into a canonical form of the matrix.

A: Given quadratic form 3x2+5y2+3z2-2yz+2zx-2xy.

Q: The mxn zero matrix , denoted by 0mn or simply 0 , is the matrix whose elements are all zero , find…

A: A matrix is a mathematical object containing numbers arranged in rows and columns. The matrix in…

Q: Since it is, find the matrix P ^ -1 by using the adjoint matrix of the P matrix.

A: We are given that  We need to find the inverse of p-matrix

Q: Find an elementary matrix E that corresponds to the row operation of subtracting – 6 times Row 1…

A: Applying elementary row operation on identity matrix I we get the elementary matrix E.Now we find a…