Find a matrix P that diagonalizes 10 0 A = 1 20 -3 5 2

Q: Find the nullspace of the matrix

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Q: . Find the rank of the matrix : 3 2 11 3 4 3 -1 2 2 Find rank of matrix

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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: Find the LU-factorization of following matrix. 1 2 3 8 14 2 6 13 4 A =

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Q: Find the diagonal line matrix P 7 -5 0 4 -1 A = 2 8 -3

A: Given the given matrix is A=57-504-128-3

Q: 3. Diagonalize the matrix A = 1 -3 3 3 3 -5 -3 3 1 if possible.

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Q: Find column rank, nullity, and the nullspace of the matrix 1 2 1 2 5 1 1 0. 3 7 2 2 -2 4 9 3-1 4

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Q: Find the matrix A if 21 . 2. 1 3 1 3

A: 21-13A =4213Now we have to find the inverse of the matrix 21-13

Q: Find a matrix P that diagonalizes A- 6.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: find an LU factorization of the given matrix.

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Q: Compute the indicated power of the matrix.

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Q: 4 1 2 5 1 3 - 7 2. 6 14 16 11 1

A: The matrix A can be written as the product of a lower triangular and upper triangular matrix . The…

Q: Find a non -2ERO 2x2 matRix A ouch +hat A2 = A=

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Q: Find an LU-factorization of the matrix.

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Q: Diagonalize the given matrix if possible: A = [1 2 0 -1

A: Our Aim is to diagonalize the matrix A=120-1

Q: (b) Find the LU factorization of the matrix: 1 -1 A= 3 -4 -2 | 2 -3 -2

A: The given matrix is                                A=1-1-13-4-22-3-2 We have to find the LU…

Q: Let the matrix A be given by -11 1. -5 0 2. -1 3

A: Given matrix is 10-11 21-50 1-100 0003 To find:  Minor M11 Cofactor C11

Q: Find the matrix A if 42 2 1 A : -1 3 %3D 1 3 A =

A: Given that, 21-13A=4213

Q: Find the innverse of the matrix b: 5 0 6 9 1 2 3 4 9 3 5…

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Q: Find A of the matrix 1- A = 2. -4 2. 1.

A: The inverse of the matrix A of order n is defined as a matrix B of order n such that AB=BA=I, where…

Q: Is the following matrix 'B' diagonalizable?

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Q: Find an LU-factorization of the matrix: show solutions. 1 1 a. 1 ⠀⠀ 2 2 2 3 2 5 b. 6 14

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Q: Find a two-by-two matrix such that: -9 5 1 0 3 5 0 1

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Q: Find the nullspace of the matrix. 1 2 -2 1 A = |3 - 5 4 1 2 3.

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Q: Find the nullspace of the matrix.

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Q: Express the matrix as a product of elementary matrices 2 2 07 [1 A = |0 L3 1 1 3 8 7 ]

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Q: Find an LU-factorization of the matrix : 4 1 2 5 1 2. 3 - 7 6 14 16 11 1

A: Recall: LU factorization by using Gaussian Elimination method

Q: Find the LU-factorization of following matrix. 1 1 2 3 5 4 6 8 1 A =

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Q: Compute the indicated power of the matrix.

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Q: Enter a 3×3 symmetric matrix A that has entries:  a11=0 a22=2 a33=5 a12=4 a13=3 a23=1

A: Symmetric Matrix : If A be an n×n square matrix , then A is symmetric if aij = aji ; where 1≤i,j≤n .

Q: Identify a matrix P that diagonalizes 2 6 A = a. 1 P = - 2 Ob. P = -1 0 0 2 Oc. P = 01 1 2 O d. -2 P…

A: Solution

Q: Find a matrix with no zero entries that commutes with the given matrix A. 4 17 1 4

A: The detailed solution is as follows below:

Q: Q3. Diagonalise the matrix [A]. 4 33 [A] = 3 6 1 3 1 6

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Q: Consider matrix [2 1 3 A = 3 -1 [2 1 1 30] Find the input matrix for the output matrix 20 [10]

A: For the given matrix A and b we have to find matrix x such that Ax=b So Input matrix is b and output…

Q: Determine the matrix A x 1, if A=(13) and 1=(9)=

A: Given A=-1043,     I=1001   To determine: the matrix A×I

Q: B: find A of the matrix 2 1 3 3 2 -1 -4 3 -1

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Q: Find a non-zero, 2 x 2 matrix such that: -5 -5 25

A: Solution

Q: Find an LU-factorization of the matrix A 2 11 -6 6 4]

A: Given, A=-21-64

Q: Find the nullspace of the matrix

A: We have given the matrix;

Q: Find the matrix A if 2 1 A = 4 2 %3D -1 3 1 3 B3: A =

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Q: Find an LU factorization of the matrix A (with L unit lower triangular). 6 4 A= 12 5

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Q: Find an LU-factorization of the matrix.

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

A: Given that, A = LU

Q: Determine the dimension of the matrix. 17 15 0 50 3 3 0 1 6 7

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Q: Find column rank, nullity, and the nullspace of the matrix 1 2 1 0 2 5 1 3 7 2 1 2 -2 4 9 3 -1 4 |

A: The nullity of a matrix A is the dimension of its null space: nullity(A) = dim(N(A)). It is easier…

Q: Find the matrix A if 4 1 A -1 3 2 3 1 4

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Q: Consider matrix [2 1 A = 3 2 l2 1 -1 1. [30] Find the input matrix for the output matrix 20 lio]

A: Given matrix  A=21332-1211

Q: (0 8 1 1 4 -1

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Q: Find a QR factorization of the matrix 1 3 -1 -3 1 2 3 1 2 1 5 8.

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