Suppose A +A+I-0 where A is a square matrix then A= A -A-I -2A A-I CS Scanned with CamScanner

Q: A is a 4 by 4 matrix with 1 's on the diagonal and -a, -b, -c on the diagonal above. Find A - 1 for…

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

A: We have to find L and U matrix.

Q: Find the characteristic equation of the matrix by inspection. 4 2] -6 0 0 6 0 0 5] 4 -9 LO

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Q: [4 -2] Let A be the matrix 1 Compute A50 1

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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: 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: The matrix is not invertible for what value of x 2 1] 3 2 1 1 2

A: The matrix is not invertible the determinant of matrix should be zero.

Q: find an LU factorization of the given matrix.

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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: 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 the SVD of matrix A [1 2 3] A= 2 4 5 L3 5 1.

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Q: Find the greatest value of A that make the matrix 2 – A 2 A singular. -6 5 – A

A: Eigenvalues and determinants

Q: If a 6 x3 matrix A has rank 3, find nullity A, rank A, and rank AT. nullity A = rank A= rank AT=

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

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Q: Let A 1B = 5 l, and C-1 = If X is a matrix that satisfies: %3D %3D 2B = Al2 - XC then X is

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Q: find an LU factorization of the given matrix.

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Q: Suppose that we use the LU-decomposition of a matrix A as displayed below to solve Ax = b in two…

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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 LU factorization of the given matrix.

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Q: Let A be 7×9 matrix. Knowing that Rank (A) 3. Then Nullity(A) is equal to: ||

A: Rank nullity theorem Let T:V→W  be a linear transformation on finite dimensional vector spaces over…

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

A: Consider the given nonsingular matrix: Here the objective is to find the elementary matrix whose…

Q: If matrix A, B and C are invertible matrix of same order then (ABC)^(-1) = * C^-1) x B^(-1) x A^(-1)…

A: Given that A,B and C are invertible matrices of the same order.

Q: 2 Discuss whether the matrix A 1 2 0 is diagonalizable or not. -3 5 2 ||

A: A matrix is said to diagonalizable if for every eigen value's algebraic multiplicity is equal to its…

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

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Q: Find a 3 × 1 matrix x with entries not all zero such that

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Q: Find the characteristic equation of the matrix by inspection. 2 -5 9 6 -3 0 0 4 0 0 8

A: Given that: 2-5960-30000400008 The characteristics equation is given by the formulas, detA-λI=0

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 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: Suppose A is a 3xn matrix whose columns span R3. Explain how to construct an nx3 matrix D such that…

A: Please check step 2 for the solution.

Q: Show that if a 3×3 matrix A is never sad then the entries along its diagonal, i.e. a11, a22, a33,…

A: Let 3×3 matrix A is never sad

Q: What is trace of matrix (2A+3B)

A: Find the trace of the matrix(2A+3B)

Q: Show that the matrix A = singular. 1 -2 3 4 0 5 0 is 60

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Q: Suppose A is invertible and you exchange its first two rows to reach B. Is the new matrix B…

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Q: (4) Let A be a 3x3 matrix. If |4|= 2 , then |3.4|=,

A: Given that A be a 3*3 matrix and |A|=2. To find the value of |3A|

Q: Let A be 5x1 matrix. Knowing that Rank (A) = 2. Then Nullity(A) is equal to: O 2 ONone of these

A: The solution is given below in the next step:

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: 2) Find the rank of the matrix A = 2 3 -1 ー1 1- ー2 -4 3. 3 -2 3. By deducing imto Echelon form.

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Q: If we multiply a row in a matrix A by a real number r, JAl changes in r.

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Q: If a 4x7 matrix A has rank 2, find nullity A, rank A, and rank A. nullity A =| rank A = rank AT

A: The given question has been solved in step 2.

Q: Let matrix A be 2 by 2 matrix and 1 A. 4 and 1 4 .2) 2 Then what is A=? ||

A: At first we will suppose a matrix A as 2x2 matrix and simplfy second condition by pre multiply by A…

Q: 3 (i);- 2

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Q: 6. Give an example of two matrices, A and B, neither of which contains any zero entries whose…

A: Below mentioned a example related to this, you can construct many.

Q: Find the greatest value of A that make the matrix 2 – 9 – A - A singular. – 6 -2 – X.

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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: Suppose A is a 4 x 4 coefficient matrix. If possible, find the entries of a matrix T that perform…

A: T is called elementary matrix. It can be obtained by performing given operation on identity matrix

Q: 29 What numbera in A-L makes A-QA@ possible (where Qis an orthognael matrix and A is an Zero or 1??

A: We shall solve this question by just using the definition of an orthogonal matrix. We know that a…

Q: Show that (-A) T= -A", where A is a 2x3 type matrix (you can show it on the example)

A: Let matrix A=abcdef. Order of matrix A is 2×3. ⇒-A=-a-b-c-d-e-f ⇒(-A)T=-a-d-b-e-c-f  →Result 1

Q: 2 Let A = 1 Compute 6I2 - A and (6I2)A. 3 - 3 61, - A = (Type an integer or decimal for each matrix…

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Q: Find the nullspace of the matrix given as; A=[1 -2 1; 2 -3 5; 1 0 7]

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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…