Show that if D = diag(A1, 12, ..., An), then the matrix VD = diag(/A1, Az, ..., VAn) is a square root of D.

Q: Construct a 3 x 3 triangular matrix A so that 1] the vector 2 is in Col A. 3]

A: We know every lower or upper traingular matrix is a triangular matrix.

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 Lunit lower triangular). 4. A = -4 -3 L U

A: We have to find L and U matrix.

Q: Let A and B be n × n nonsingular matrices. Find nonsingular matrices P and Q so that PAQ = B .

A: Given that the n×n non-singular matrices as A and B. It is known that a matrix is non-singular only…

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

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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 matrices P and D so that A = PDP1 and D is a diagonal

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Q: Show that if A is an upper triangular matrix, then A T is lower triangular.

A: A is an upper triangular matrix. That is, Now let A=aij be a n×n upper triangular matrix. Then,…

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: 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: ) Consider the matrix A = [a b] with a, b, c and d real-valued numbers. Under which condition(s) for…

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Q: Show that if A is a symmetric matrix, then Ak , k = 2, 3,... , is symmetric.

A: Given that, A is a symmetric matrix. Then we get, A^T = A; where A^T is the transpose of matrix A We…

Q: Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple…

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Q: Denote the column vectors of the matrix 11,922.. , ann +] True, false, or uncertain: a; is…

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Q: Find an SVD of the indicated matrix.

A: The matrix is given of which SVD is to be calculated so,

Q: Show that if A is an orthogonal matrix, then A−1 is orthogonal.

A: Explanation: Given that,  A is an orthogonal matrix.

Q: Show that the column vectors of following matrix A are linearly independent:

A: the given question is taken from the matrix in which we have to find show that the given matrix A is…

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: and that h(T) = T² – 2T – 7, find h(A). The questions should read as attached. Change made at the…

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

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 diagonal matrix D is similar with A a A =[? -5 And make sure can transtor diagomalizablewith

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Q: Show that the matrix; is singular

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Q: Find the inserve if it exists, of the following matrix. 1 -1 2 1 1 1 1 2

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Q: Find the inserve if it exists, of the following matrix. 1 2 1 1 1 2

A: The give matrix  is, 1 1 -1 2 -1 1 1 1 2 The determinant of the above  matrix is,…

Q: If xER" is a column vector (i.e. an n ×1 matrix), then In-2xx' is always a symmetric matrix. True…

A: Consider the given column matrix as x=x1x2⋮⋮xn-1xn, x∈Rn. Compute the transpose of the matrix x as…

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: () (:) Find the matrix A satisfying A and A and write the SVD of A in 2. vector form. [Hint: Start…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Show that if A is an upper triangular matrix, then AT is lower triangular.

A: Given, A is an upper triangular matrix

Q: Let A = UEVT be a SVD of a square matrix A. What is the product of the diagonal elements of E, in…

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Q: Let r1, .. r,be vectors in R", and let Q be an m xn matrix. Write the matrix Qr, Qr, as a product of…

A: Given:Let r1.......rp be vectors in ℝnLet Q be an m×n matrix Qr1.......QrpR=r1.......rpQ=Q…

Q: find if the vector x is in the range for matrix A

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Q: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

A: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

Q: Let B = and B' = Find the change of base matrix from B' to B and from B to B'

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

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

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Q: If a vector is in the range of a matrix A, then it is also in the null space of A. true of false?

A: Answer

Q: Let A be an n x n matrix and let D be a n x n diagonal matrix. Show that AD =…

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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: Let A be an m × n matrix. Show that ATA and AAT are both symmetric.

A: Given A be an m×n matrix. we have to show that ATA and AAT are both symmetric.we will make use of…

Q: If A is a 3 x 3 matrix and a1 + 2a2 a3 0, then A must be singular, where a1, a2, a3 are column…

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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: Show that if a square matrix A has two equal columns, then A is not invertible.

A: since not a particular question asked ,as per guidelines solution to only first question (i.e Q1) is…

Q: Show that if B is a symmetric nonsingular matrix, then B2 is positive definite.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: If U is a square matrix such that UTU I, what can we say about det (U)?

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Q: 20. Can every vector in R* be written as a linear combination of the columns of the matrix B above?…

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Q: Construct a nonzero 3 × 3 matrix A and a nonzero vector b such that b is in Col A, but b is not the…

A: We will construct A and put b as a linear combination of column vectors in A.

Q: and D be a diagonal matrix D = diag(A₁,..., An) such that

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Q: Since it is, find the matrix P ^ -1 by using the adjoint matrix of the P matrix.

A: We are given that  We need to find the inverse of p-matrix