Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix 2x -y = 5       x + 3y = -1

Q: Find a (2x2) singular matrix A that maps (2, 4) into (3, 1).

A: Singular matrix mean its Determinant is equal to 'zero' .

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: 2x1- 3x2+ 2x3= 9 3x1- 2x2+ X3 = 4 X1 - 4x2+ 2x3 = 6

A: Given system of linear equations is ,                        2x1-3x2+2x3= 9…

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 2 -4 A = 4-4 3. - 1 18 -3

A: The LU factorization of a matrix A is writing A as the product of matrices L and U, where L is a…

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

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Q: Find the matrixx such that 2A + B + X =0 where 1 2 3 -2 A = %3D 3 4 1 5 Select one: a. -1 -2 -7 13

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Q: a) Show that there is no matrix A E M250x250 with real entries satisfying AAT = -I.

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Q: Find the symmetric matrix A associated with the given quadratic form. 2x2-3y2-z2-4xy

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Q: Find three non-trivial 2 x 2 matrices such that the square of the matrix is the zero matrix, i.e: A?

A: We want to find matrix A such that A2 = 0000

Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

Q: Find x such that the matrix is singular. 4 X A -2-6 X3D

A: Given Matrix is, A=4x-2-6 we know that, A matrix is said to be singular if it's determinant is zero.…

Q: Find an SVD of the indicated matrix.

A: The matrix is given of which SVD is to be calculated so,

Q: which of the following is the cofactor A13 of matrix?

A: Simply omit that raw and column whose co-factor matrix required and write rest all elements in same…

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 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 the coordinate matrix of X relative to the standard basis for M3,1.

A: To determine: The coordinate matrix of X relative to the standard basis for,

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 the change of basis matrix from B1 to B2. -1 2

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Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

A: Given matrix, 210112021

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: : Find the inverse of the matrix 1 1 -1 0 -2 1 A = 3 -1 2 with using the method of Cofactor…

A: firstly find cofactor of A and then adjoint and use  A-1 = adjA/|A|

Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

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

A: Sol

Q: Use the method of Example 6 to compute the matrix A10, where 1 0 6 2 A =

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Q: Find the inserve if it exists, of the following matrix. 1 -1 2 1 1 1 1 2

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Q: Use the method of Example 6 to compute the matrix A10, where 1 0 A = -3 2

A: The given matrix is A=10-32. Observe that, A2=10-32 10-32=10-94=10-3·22-122A3=10-94…

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 1 -1 A =0…

A: Given,

Q: Verify by finding the matrix of S 0 T (a) by direct substitution and (b) by matrix multiplication of…

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

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Q: Find the inserve if it exists, of the following matrix. 1 2 1 1 1 2

A: The give matrix  is, 1 1 -1 2 -1 1 1 1 2 The determinant of the above  matrix is,…

Q: Compute the standard matrix for the linear map T : R² → R² which (1) rotates i by 0 = T, (2)…

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Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 1 -1] A…

A: NOTE:We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find Q and R in the matrix factorization 3 2 4 1 -1 QR. %3D [0 0 As usual, Q is an orthogonal matrix…

A: Given

Q: Find x such that the matrix is singular.

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Q: Explain transpose AT of the m x n matrix A?

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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: find a 3 x 1 matrix x with entries no all zero such that Mx = 1x and            [ 1 2 -1 M =…

A: Consider a system of homogeneous equations. A system of equations can be solved by eliminating some…

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 3 -4 -3 L = U = A,

A: The solution is given below

Q: 6 X1 -1 -5 X2 II

A: Let us consider the system of differential equation X'=AX then the solution of system of equation is…

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: The matrix H1, as any Householder matrix, has the form H1=l-2ww', for some vector w. The value of…

A: In order to apply the first step of QR-factorization to A, check for the first column of A. The…

Q: Given the matrix 6 0 0 A= 0 2 2 0 2 2 find an orthogonal diagonalization of A: A = QDQ"

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Q: Determine the standard matrix of a reflection in R² in the line 3x1 + 4x2 = 0. %3|

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Q: Find a 3x1 matrix X with entries not all zero such that AX = X , where [1 0 -1] A =1 0 1 4 -4

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Q: Find all a and B >0 so that the matrix B = 23 6 2 is diagonally dominant;

A: A square matrix is diagonally dominant if   for .

Q: Determine the standard matrix of a reflection in R2 in the line -x1 + 2x2 = 0.

A: Given line is -x1+2x2=0

Q: Find x such that the matrix is singular.

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Q: (b) Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 3.…

A: Given :          A = 13-223001-1   To find the inverse of A. Also, to compute 3A-1.

Q: Find x such that the matrix is singular. A = -3 -6

A: