Consider the following matrix: -31 A = -3 -4 9. 1 -2 (a) Verify that A is diagonalizable. (b) Find the matrix P that diagonalizes A. (c) Determine the diagonal matrix P-'AP = D.

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

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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: Let A be an nxn matrix and B= A+ I, where / is the identity matrix, then it is possible for A and B…

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

Q: Determine if the matrix, M is diagonalizable. Show your complete solution. 25

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Q: Find an SVD of the matrix. -7 3 A = - 3 - 1 O (Type an exact answer, using radicals as needed.) A =

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Q: Under what conditions will the diagonal matrix be invertible? Assume that A is invertible and find…

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Q: 1. By hand, find the QR factorization of the matrix

A: QR factorization means A = QR Where, Q is an orthogonal matrix with orthogonal columns and R is an…

Q: Explain why the matrix A + C does not exist.

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Q: Calculate the matrix P, the matrix D, det(P), and the matrix P! Is the matrix A2 diagonalizable?…

A: Solution:-

Q: Let the matrix below be Anti-symr

A: Anti symmetric matrix is also known as skew symmetric matrix.

Q: If the matrix A is positive symmetric definite, is BTAB also positive symmetric definite?

A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

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 an orthogonal matrix Q and a diagonal matrix D

A: Follow the procedure given below.

Q: The 2 ´ 2 identity matrix is:

A: To find:

Q: Find an LU factorization of the matrix A (with Lunit lower triangular). 4 A= 12 2 -0 12 8 4,

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Q: Which of the following matrices is not in Row Echelon Form (REF)?

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Q: If the Reduced echelon form of A-λI is the identity matrix then what is the eigenspace (Eλ)?

A: We need to find the eigenspace (Eλ) if the Reduced echelon form of A-λI is the identity matrix. Note…

Q: Is it possible for A3 to be an identity matrix without A beinginvertible? Explain.

A: To explain:It is possible for A3 to be an identity matrix without A being invertible.By definition

Q: What is the name of the matrix, Sij?

A: Sij is called as similarity matrix.

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

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Q: Let A be a 4 × 4 real symmetric matrix witheigenvaluesλ1 = 1, λ2 = λ3 = λ4 = 0 What type of matrix…

A: Given, A is a 4×4 real symmetric matrix with eigenvalues 1, 0, 0, 0. Now we have to find what is the…

Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

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Q: 3. Find all matrices which satisfy the matrix equation (::)(; })-(; :)(::)

A: Here,

Q: DEMONSTRATE THAT A A-1= A-1A = I      FOR THE MATRIX BELOW     1 -1 2 2 -3 4 1 0 3

A: Given matrix A=1-122-34103 We have to  prove that AA-1=A-1A=I We know that A-1=AdjAA

Q: Find x such that the matrix is singular. A- -2

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

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Q: 32. Construct a nondiagonal 2 × 2 matrix that is diagonalizable but not invertible.

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Q: Find the standard matrix for the linear operator T: R^3 --> R^3 that first rotates a vector…

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Q: What does it mean to say that A is a matrix with dimensionm  n?

A: A matrix is a rectangular array of elements arranged in rows and columns. The size of the matrix is…

Q: FIND THE FUNDAMENTAL MATRIX AS W ELL AS THE FUNDAMENTAL MATRIX SATISFYING )- I x'= -4 %3D

A: For the solution follow the next steps.

Q: Find the inverse of the matrix by Gauss-Jordan Elimination (using an adjoined matrix). (If an answer…

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Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: What is the condition for a diagonal matrix to be orthogonal?

A: use the properties of orhtogonal with respect to a diagonal matrix...

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

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Q: Suppose A = UDVT where U and V are n x n matrices with the property that UTU = I and %3D vTV = I,…

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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: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

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Q: Find the inverse of the matrix and verify that A-!A = AA1- 1. 4--10 A 3D 2. 8. A-1 Show My Work…

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Q: 1- the rank of the matrix A.

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Q: Suppose A is a 2 × 2 matrix which rotates every vector clockwise by 45degrees . Geometrically, what…

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Q: Let A be a nilpotent matrix of order n then A*n = 0 ) nxA = 0 A =nx1, l is Identity matrix

A: A be a nilpotent matrix of order n

Q: Let A be an nxn matrix and B= A+I, where / is the identity matrix, then it is possible for A and B…

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Q: Find an LU factorization of the matrix A. 3 -1 3) A- - 18 1 0][ 3 1 A) A= B) A = 10 3 -1 0-3 -6 1 0…

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

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.