Find a basis for the subspace of Mnxn consisting of all diagonal matrices.

Q: M2,2 is the vector space of all 2 x 2 matrices. List the o element of this vector space.

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Q: Determine whether the set of all 2 x 2 nonsingular matrices, together with matrix addition and…

A: See the solution below.

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: Consider the 2 X 2 matrices A1 = 1 1 A2 = 0 1 A3 = 0 0 A4 = 1 0 1 1 1 0 () Argue whether these four…

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Q: Show that the matrix is skew – Hermitian and hence find the eigen Values and eigen vectors

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Q: what is a Hermitian matrix? does every Hermitian matrix has to be square matrices?

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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: Consider all 4 by 4 matrices A that are diagonalized by the same fixed eigenvector matrix X. Show…

A: Given: Matrices, A of order 4×4 with eigenvector matrix, X.We need to show that A form subspace cA,…

Q: find a matrix that column space is spanned by fewer vectors than there are columns in the matrix

A: The idea is the create a matrix such that one of the columns is in the linear span of the other two…

Q: What is a singular matrix

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Q: Show that eA is nonsingular for any diagonalizable matrix A.

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Q: Find an orthogonal diagonalization for A = 1 0 1 0 1 -1 (1888) -1 1 i.e. find an orthogonal matrix U…

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Q: Let A and B be two skew-symmetric matrices of the same size. Show that AB+BA is symmetric.

A: Given that: Let A and B be two skew-symmetric matrices of the same size. To show: AB+BA is…

Q: Explain the flop count (number of multiplications and divisions uvT A = uTv whereu and v are alone)…

A: The flop count of the operation represents the cost of the computation of an operation. One…

Q: If the subspace of all solutions of Ax 0 has a basis consisting of two vectors and if A is a 5x7…

A: The matrix A is a representation in the standard basis of the linear transformation, f:ℝ7→ℝ5, x↦Ax

Q: a) Decompose the coefficient matrix A into lower and upper triangular matrices.

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Q: Write a second degree equation matrix and prove that it is in vector space?

A: To show: An example of a second-degree equation matrix which is in vector space.

Q: Find the singular values of the matrices in Exercises

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Q: Calculate matrix representation based on standard bases

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Q: Can the null space of a 3 × 6 matrix have dimension 2? Explain.

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Q: 2rị + 13 T: R' → R?, T 21, 22, 13, L4 ER -12 - 3r4

A: Given  and the standard bases are given by

Q: Does the set of all 2x2 matrices form a vector space, please explain.

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Q: Use matrix multiplication to find the contraction of (a,b) with factor k =1 / infinity, where…

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Q: Q2. Show that M2x2 , the set of all 2× 2 matrices is a vector space. Explain your answer? Good Luck!

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Q: The set of all 2x2 symmetric matrices is a vector space Select one: True False

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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: Notations That Represent A Line

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Q: Define Hilbert matrix.

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Q: Define invertible matrix.

A: Definition: A square matrix of order   is said to invertible, if there exists an square matrix B…

Q: Describe all 1 by 1 and 2 by 2 Hermitian matrices and unitary matrices.

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Q: Show that a triangular matrix is normal if it is diagonal

A: Given: A triangular matrix is normal.if it is diagonal