Find the characteristic values and characteristic vectors of the matrix [8 − 6 2 − 6 7 − 4 2 − 4 3 ]

Q: a) If a 7 × 5 Matrix A has rank 2, find dim(Null A), dim (Row A) and rank AT

A: 1) Given  7×5 matrix  rank(A)=2 using rank nullity theorem we have rank A + null A= number of…

Q: Find an LU factorization of the matrix A (with Lunit lower triangular). 4 -8 8 -4 A = 8 - 14 11 -5…

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Q: Find the characteristic equation of the matrix: 4 C = 2 -2 2.

A: Characteristic equation of the matrix C is given by  det ( C - λI ) = 0

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

A: First, define the matrices L and U . Let, the matrix L be defined as L=10l211 Let the matrix U be…

Q: Find an LUfactorization of the given matrix.

A: Find an LUfactorization of the given matrix.A=2-431

Q: Let A = - 2     1    0                 1     0    1                2    -3    1        A is a…

A: trace is the sum of all diagonal elements of the matrix.

Q: Find an LUfactorization of the given matrix.

A: Given, To find LU factorization of the given matrix.

Q: Find an LUfactorization of the given matrix.

A: To Determine: find an LU factorization of the given matrix  Given: we have a matrix12-3-1…

Q: Find an LUfactorization of the given matrix.

A: Let A=123456879. L and U are the lower triangle matrix and upper triangular matrix respectively. In…

Q: Find x and y such that the rank of matrix A is 2. 1 0 a – 1 0 у- 2 г+1 -5 A = 4 x = Ex: 5 Ex: 5 С y…

A: We are using rank nullity theoram  Rank(A) + nulity(A) = number of coloumn in A.

Q: ) Find a matrix A such that 3 A -3 1 1 EEE A =

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Q: A symmetric matrix A is positive def

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Q: Consider the following matrix and vector: 1 1 A = 1 -4 0 -3 -2 and x = 6

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Q: Find the characteristic values and vectors of given matrix shown below. 1 -1 -1 A= 1 0 3 1 3.

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Q: [1 2 2 3 1 0 1 1 4 4

A: Given matrix is  123101144find LU factorization of a given matrix

Q: Find an orthogonal basis for the column space of the matrix to the right. - 1 7 3 -6 4 2 -1 1 -5 -2

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Q: [1] Construct a 3 x 3 nonzero matrix A such that the vector |2 is a solution of 3. Ах 3D0

A: A vector is given let x=123 To find: A non-zero 3×3× matrix,A=a11a12a13a21a22a23a31a32a33

Q: Find x such that the matrix is singular. [ х 7 A = -5 2 X =

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Q: Examine the nature of the following matrix defined by A = [0        1 + 2i       −1 + 2i      0  ]…

A: Given:  A=01+2i−1+2i0 To explain nature of above matrix and to find its proper values and proper…

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: Determine the Householder matrix that annihilates all but the first entry of the vector v = [2 22…

A: Let α=2222T Then take, v=α-αc1=2222-α2000=2222-α000 ,Here α=±||a||2=±2 Now , since,α1  is positive ,…

Q: (2) Let A = UDV" be a SVD of a square matrix A. What is the sum of squares of the singular values,…

A: We find the sum of squares of the singular values in terms of A.

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

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Q: 3. What is the dimension of the vector space consisting of five-by-one column matrices where the…

A: Option B i.e 4

Q: Show that the matrix 2 1 A = 1 3 2 1 1 1 is invertible, but that A cannot be written as the product…

A: Solve the given problem.

Q: Г1 3 2 5 1 [3 4 2

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Q: If an nxn matrix is invertible, then the column vectors form a basis for R

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Q: (3) If A is a real 2 by 2 matrix, A-(::) a b and a is a two-dimensional column vector, what…

A: Please check step 2 for the solution.!

Q: Construct a 3 x 3 matrix A with every entry non-zero such that the following vector b is in the span…

A: See the attachment

Q: (b) triangular with l's on its diagonal, and U is upper triangular. Use the results in (a) to obtain…

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Q: The order of the single matrix obtained from 1 1 -1 To 1 23 is 1 0 21 -1 0 2 2 0 3 2 (a) 2 x 3

A: Here the order of the matrix needs to find out for both terms. Subtraction and addition won't affect…

Q: A real square matrix Q is called orthogonal if QTQ = I. Prove det(Q) = ±1. Give an example of such a…

A: Solution

Q: Find the change-of-coordinates matrix from B to the standard basis in R". 2 -2 3 8 -2 7 8. Pa

A: Uf7ygth

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: 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: 1 2 3 A = 1 3 2 2 6 8

A: See solution below

Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(4, 3, 3), (-11, 0, 11), (0,…

A: The given vector space is  with basis B'=4,3,3, -11,0,11, 0,9,2. Consider the vector x=26,3,-19∈R3.…

Q: 3- If x=[ 26 12; 15 6 3; 10 11 1], then a) replace the first row elements of matrix x with its…

A: X=[  2 6 12;15 6 3;10 11 1]

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: 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: 48. Construct a 3 x 3 nonzero matrix A such that the vector 1 -2 is a solution of Ax = 0.

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

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Q: Determine the dimension 31 43 -8 21 Ab X of the matrix. AN

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Q: Find the change-of-coordinates matrix from B to the standard basis in R". 6. -4 2 B= 5 -4 7. -3 7…

A: Solution

Q: [5 Let B =E dl: Is the matrix B orthogonally diagonalizable? If yes, find a diagonal matrix 2 0…

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Q: The aim of elimination steps in Gauss elimination method is to reduce the coefficient matrix to a)…

A: A matrix where the number of rows is equal to the number of columns is said to be a square matrix…

Q: a) Prove that the matrix A = is diagonalizable if –4bc (a– d)². What happens when –4bc = (a– d)² ?

A: Given,         A= abcd

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