1. a)Determine E, a product of elementary matricesm which when premultiplying A performs a Gauss-Jordan pivot on the (3,3) entry of A=[1 0 -1 6, 0 1 2 7, 0 0 2 4]  b) Find product EA. It should be in reduced row echelon form.

Q: Construct a 2 x 3 matrix A such that the solution set of the equation Ax = 0 is a line in R3.

A: a)       Result of a system with 2×3 coefficient matrix is a line when system has one free variable.…

Q: 1) Construct the matrix A =(a;;) where 3x2 ) aj = i+j, if i = j,and Li-j, if itj %3D

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Q: Consider 12 1 2 13 -1-3 4 Convert A to an upper triangular matrix U by using Gaussian elimination…

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Q: 6. If A is an nxn matrix whose LU decomposition is PA = LU, , prove that det(A) = (-1)' u₁₁ U 22.²…

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Q: 2. Suppose A is a square matrix. Which matrix is not symmetric? O A+AT O AAT ОА-АТ O ATA

A: Note the following results if A and B are two matrices ABT=BTAT…

Q: Show that if A is an upper triangular matrix, then A T is lower triangular.

A: A is an upper triangular matrix. That is, Now let A=aij be a n×n upper triangular matrix. Then,…

Q: Consider the Az 1 34 17 9 203 2 8 16 6 0 5 /

A: (a) We know that we can find the determinant of the matrix by expanding along any column or row.…

Q: highlighted" condition. A matrix in M2(R) which is “nilpotent" and has a non-zero entry in each row…

A: A matrix is Nilpotent if Ak = 0 where 0 is null matrix and k is index of matrix A.

Q: 2 14 Wiite the and system below as Vertor euation. matrix Quatan +6z =0

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Q: 1) Find a diagonal matrix A that satisfies A-2: [2 0 0 1/4

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Q: 5. Find a dlagonalizes the fouowing natrlx A, and determine the diagonal matrix D = p'AP matrix p…

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Q: 6. (a) Find the matrix A so that AB=C, where C1 C2 C3 b, b, bz 2 B= b, b2 b3 & C= C1 C2 C3) а, а аз…

A: AB=C

Q: 4) The Cayley-Hamilton Theorem states that every square matrix satisfies its characteristic…

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Q: 1. Suppose u and v are any two solutions of the linear system with matrix equation Ax = b. Prove…

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Q: 6. If A is an nxn matrix whose LU decomposition is PA=LU, prove that det(A)=(-1)' u₁22... Un where r…

A: Given: A is an n×nmatrix, whose LU decomposition is PA=LU.   To show: detA=-1ru11u22...unn, where r…

Q: Find three values of c for which the matrix C is not invertible.

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Q: 1-If x= [ 2 6 12; 15 6 3; 10 11 1], then a) replace the first row elements of matrix x with its…

A: The average of n digit can be obtained by dividing the sum of the digits by the number of digits…

Q: Given the input coefficient matrix for a hypothetical economy made up of only two industries as A…

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Q: (a) Let A be an m × n matrix, and let B be the result of performing a single elementary row…

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Q: If A is a 6 × 8 matrix, what is the smallest possible dimension of Nul A?

A: Consider the provided matrix, Given, A is a 6 x 8 matrix. Since, the rank of A equals the number of…

Q: [1 1 Show that the matrix A is not diagonalizable.

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Q: 5. Suppose that the augmented coefficient matrix of Ar = b is (1 3 1 -1 0 bị 2 6 1 4 12 3 -2 1 ba 1…

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Q: Enter a 3 x 3 symmetric matrix A that has entries au = 5, az2 = 4, a33 = 0, a12 = 2, a3ı = 1, and…

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Q: (a) The matrix ( (AB)-1 )T comes from (A-1 )T and (B-1 )T In what order?(b) If U is upper triangular…

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Q: 5. Find a dlagonalizes the focowing matrix Á, and determine the diaganal matrix D = p'AP matrix p…

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Q: 4. A matrix A is similar to matrix B, if for some invertible matrix P, B = P'AP. Is B similar to A?

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Q: (1) A= BCB, where C is an n x n symmetric positive-definite and B is an n x n symmetric matrix;…

A: In part l, We are given that A=BCB Here, C is n×n symmetric positive-definite. So, xTCx>0 with…

Q: 1. Show that matrix A is singular 1 2 A= 3 -1 -2 3 -2

A: Given  A=1203-12-23-2

Q: 1 4 What is a, if A = is a singular matrix ? %3D 2 a

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Q: Consider the augmented matrix 1 2 0 3 5 -1 6. 17 2 4 1 2 12 2 0 0 -7 11 Enter the value of the pivot…

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Q: 2. Consider the 6 x 8 matrix [1 30 0 0 0 10 -3 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 5 6. 4. 0 -7 8 -9 A…

A: The dimension of ColA is the number of pivot columms in the corresponding echelon form of A. If A is…

Q: 6. Prove that the matrix A = -1 2 is diagonalizable, and find the corresponding diagonal matrix D…

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Q: If the null space of a 5 × 6 matrix A is 4-dimensional, what is the dimension of the row space of A?

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Q: If the rows of an mxn matrix A are linearly independent and Ax=b is consistent then it has unique…

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Q: 1. Show that matrix A is singular [1 2 0 A= 3 -1 2 -2 3 -2

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

Q: If an nxn matrix A is invertible, then the rowa of A' are linearly independent. T O True O False

A: If a matrix is invertible then its rows are linearly independent

Q: 1. P.ove that matrıx multıplication is associative. Show that the product of two orthogo- nal…

A: The second part of the question is proved in the claim.

Q: Find the minor M12 and cofactor A12 of matrix A. 1 6 A = 3 3 -2 0 1 8.

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Q: Find a Matrix P that nationalizes A, and check your answer y computing PDP¯1 0 00 0 0 0 30 1

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Q: 1.28 Show that the nonzero rows of an echelon form matrix form a linearly indepe

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Q: 4- Which of the following is the basis of the Gaus-Jordan method used in the solution of linear…

A: Gauss Jordan Method is a classical method to solve system of linear equations.

Q: (a) Let A be an m × n matrix, and let B be the result of performing a single elementary row…

A: We have to prove that following Statement.

Q: et A be the following matrix 2 7 2 4 4 8 2 3 3 fter diagonalization, Pand Dare found such that A =…

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Q: Prove the corollary to Theorem 3.16: The reduced row echelon form ofa matrix is unique.

A: Given: Theorem: The reduced row echelon form of a matrix is unique.

Q: 2.3 Compute the principal square root of each of the lowing positive semidefinite matrices. (b) 2 3…

A: We shall solve first question only as you have asked more than one Que of same type. For others…

Q: If U is a square matrix such that UTU I, what can we say about det (U)?

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Q: If A is a 2 x 2 skew symmetric matrix, must det(A) = 0?

A: we have a 2×2 skew symmetric matrix.

Q: 1) Find a diagonal matrix A that satisfies A-2 20,

A: Here, we need to find a diagonal matrix A such that A-2=2004