While practicing computations in MATLAB, you find a 3 x 3 matrix A and vectors v, w with Av = v, Aw = w and v x w + 0. Determine if A could represent: • a projection on a line, • a projection on a plane, • a reflection across a line, • a reflection across a plane, or • a rotation. Justify your answer by providing an example of a matrix and vectors, or a reason why they can't exist.

Q: The reduced row echelon form of the matrix A is I3 . Describe all possible matrices A.

A: Consider the reduced row echelon form of a matrix A is I3. We need to determine all possible…

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: If A and B are orthogonal n by n matrices, then AB is also orthogonal. True or False? Give an…

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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: . Identify which of the following matrices is in row echelon form(REF)and/or reduced row echelon…

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Q: Diagonalize matrix A, i.e., find diagonal D and invertible P such that A = PDP-1, where -[:] 3 2 A =…

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Q: Construct a 4x3 matrix A with rank 1. Select the correct choice and, if necessary, fill in the…

A: We construct a 4×3 matrix A with rank 1.

Q: A square northwest matrix B is zero in the southeast comer, below the antidiagonal that connects (1,…

A: It's a very conceptual question and will need lots of grey matter. Please read the question…

Q: Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A.…

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Q: If A is a rank one matrix, the second row of R is ___ . Do an example.

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Q: When A is invertible, MATLAB finds A by factoring LU (where L may be permuted lower triangular),…

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Q: Find a 2x2 matrix that forms an angle of n/3 cadians with the matrix P -- (: 9) 2 0 0 2

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Q: If A is a square matrix, then Ker(A) = Ker(RREF). True or false?

A: If A is aquare matrix then we have to check Ker(A) =Ker(RREF(A))

Q: 2 -3 0 A = 5 2 1 -1 1

A: A-1=1|A|(adj. A)=1|A|A11A21A31A12A22A32A13A23A33 where Aij is the cofactor of aij.

Q: 1. Determine if the following vectors are linearly independent. Justify each answer without…

A: a) Linearly Independent Determinant of the given vectors is not equal to zero.   b) Linearly…

Q: Suppose that A is a square matrix with two identical columns. Can A be invertible? Suppose that A is…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A.…

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Q: If A is a 31x24 matrix whose rank equals 10, find dim(Nul(AT)). Your Answer:

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Q: Suppose B = QRQ-1, where Q is orthogonal, and R is upper triangular. Show that if B is symmetric,…

A: Given that B=QRQ-1 where, Q is orthogonal and R is upper triangular. Then, multiply Q on both sides:…

Q: Suppose matrix A is m×n and B is n×p. If the first row of matrix A is all zeros, what can you say…

A: Explanation:Since matrix A is m×n and matrix B is n×p, the matrix AB will be m×p.In order to get the…

Q: What is the only 3x3 matrix B such that for every 3x3 matrix A, ВА — 2A? What is the only 3x3 matrix…

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Q: Find the LU factorization of A = 10 -15 -21 That is, write A = LU where L is a lower triangular…

A: Given: 55108-15-21

Q: Let A be an mtimes×n matrix and let B be an ntimes×p matrix. If the first row of A consists only of​…

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Q: When two m x n matrices are said to be equal? Explain there Applicability?

A: Two mxn matrices are said to be equal if their corresponding elements are equal.

Q: 43. For square matrices A and B, is it true, in general, that (A + B)-1 = A¯1 + B¯!? Explain.

A: Explanation of the answer is as follows

Q: Enter the elements of a 3 * 3 matrix using the keyboard and then find the result of summing the…

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Q: The ith row vector of a matrix product AB can be computed by multiplying A by the ith row vector of…

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Q: A mX n matrix A requires the s

A: Given, An matrix requires the storage of numbers. To verify: The SVD of rank all together…

Q: A matrix that is both upper and lower. triangular is called diagonal ylgn ihi

A: Upper and lower triagular matrix

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: Use Proposition 2.50 to state Jacobi's method and the Gauss-Seidel method in matrix notation for the…

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Q: Suppose A is rectangular ( m by n) and S is symmetric ( m by m).(a) Transpose AT SA to show its…

A: Given: Matrix A is rectangular ( m by n) and matrix S is symmetric ( m by m).

Q: In general, it is difficult to show that two matrices are similar.However, if two similar matrices…

A: Given two n × n matrices, A and B, we say that A is similar to B if there exists an invertible n × n…

Q: Find the LDU factorization of -2 -2 6 4 -15 -10 A = -6 3 -13 -14 -2 14 46 35 That is, write A = LDU…

A: Given A=−2−26425−15−10−63−13−14−2−144635. Find the LDU factorization of A.

Q: Suppose that Q is a matrix with the property Q−1 =QT . Show thatqij = Qij/det(Q)

A: Given: Q-1 = QT To Prove: qij = Qij/det(Q) Formula Used: If A is a square matrix, then its inverse…

Q: For a square matrix A, AAT = ATA. %3D A) True False

A: We have to find the given statement is true or false.

Q: Consider the matrix A =

A: Given, the matrix                       A=420040004

Q: We will define a checkerboard matrix to be a square matrix A = (aj), where if i + j is even if i +…

A: For row reduced form of nxn checkerboard matrix contains 2 non zero rows only. So the rank is 2 (…

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

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Q: Consider the following matrix. Find the proper procedure for changing the ements to zero. 1 1 - 1 -5…

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Q: Suppose a 6 x 8 matrix A has four pivot columns. What is the dim (Null A)? Is Col A = Rª ? Explain.

A: see below the answer

Q: ) If A is a 5 × 4 matrix, what is the largest possible dimension of the row space of A? If A is a 4…

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Q: What are L and D (the diagonal pivot matrix) for this matrix A? What is U in A = LU and what is the…

A: In the given question, the matrix A is given as: A=248039007D=diagA=200030007

Q: Consider a matrix A, and let B= rref(A). %3D a. Is ker(A) necessarily equal to ker(B)? Explain. b.…

A: The matrix B=rrefA is the Reduced Roe Echelon form of the matrix A. The kernel of a matrix A is the…

Q: If the product AB is the zero matrix, AB = 0, show that the column space of B is contained in the…

A: Given that the product AB is the zero matrix, AB=0, show that the column space of B is contained in…

Q: If you keep the same basis vectors but put them in a different order, the change of basis matrix B…

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Q: If the n x n matrices A and B are orthogonal, which of the matrices in Exercises 5 through 11 must…

A: Given- A and B are n×n orthogonal matrices. To find- A+B is orthogonal or not?     Concept Used-…