A composite of matrices is said to be expanded if they are expressed as the sum or products of single matrices. For example, the expanded form of (AB)-', where A and B are square invertible matrices of the same size, is B-'A¬!. Given this notion of expansion, expand the following. ([AB + (CD)"] [(EF)-1 + GH]))" . All matrices A, B, …, H are square, invertible and of the same size.

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

A:

Q: Prove that if both products AB and BA are defined, then AB and BA are square matrices. Assume that A…

A: We want to prove that AB and BA are square matrices

Q: If matrix A is full row-rank, then use SVD to prove that the pseudo inverse is given by A+ =…

A: According to null matrix singular decomposition, a matrix A can be written as, A=U∑V* Then use the…

Q: Prove that a matrix that is both unitary and upper triangular must be a diagonal matrix.

A: Given that the matrix A is both unitary and upper triangular.

Q: If Q is an orthogonal matrix, prove that any matrix obtained by rearranging the rows of Q is also…

A: The matrix is said to be an orthogonal matrix if the product of a matrix and its transpose gives an…

Q: If A and B are invertible 5x5 matrices, then A+B is also invertible. True False

A:

Q: Suppose A is a symmetric nxn matrix and B is any nxm matrix Show that B'AB, B'B, and BB' are…

A:

Q: Under which conditions an inverse matrix be defined for a matrix?

A: There are two conditions for matrix to be invertible.

Q: Show that these four matrices form a representation of the Vierergruppe, whose multi- plication…

A: 17.2.2 We have to show that given matrices  I,A,B and C form a Vierergruppe. Concept:…

Q: () Write the statement of Cayley-Hamilton theorem for square matrices.

A: Cayley-Hamilton statement

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

A:

Q: Show that any nX n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

A: To show that any n x n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

Q: All elementary matrices are lower triangular matrices Select one: True False

A: The given statement is False. Because we can get elementry matrix by identity matrix by applying the…

Q: 4. Prove that the product of two upper triangular matrices is always another upper triangular…

A:

Q: If A and B are square matrices of the same size such that AB = BA, prove that (AB)2 = A2B2.  By…

A:

Q: 2 Prove that the 3 × 3 matrix A = 4 -1 cannot be factored as A = LDL". 1 -1 3

A: In the question it is asked to show that the matrix A=12124-11-13 cannot be factored as A=LDLT.

Q: If, then for what value of α is A an identity matrix?

A: We have to find the value of α.

Q: 18. Two matrices A and B are said to anticommute if AB = - BA. If A and B are anticommuting 3 × 3…

A:

Q: Show that any matrix of size 3 by 3, can be written as the sum of two invertible matrices, that is,…

A:

Q: 4 9- That is, find an -5. | Diagonalize the matrix A [3 invertible matrix P and a diagonal matrix D…

A: Given matrix A=4-63-5

Q: Show that the matrix 2 1 A = 1 3 2 1 1 1 is invertible, but that A cannot be written as the product…

A: Solve the given problem.

Q: Ч. W is the set of all 2x2 upper triangular matrices in Mzx2 (IR).

A:

Q: Show that the matrix below does not have an LU-factorization.

A:

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

A:

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

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Q: A nxn matrix is called nilpotent if there exists an integer p such that AP=On. Show that each of the…

A:

Q: andB are distinct (not equal) square matrices of the same size (n×n for some n), andA−B is not…

A: False

Q: Generalize the definition of LU factorization to nonsquare matrices by simply requiring U to be a…

A:

Q: Suppose a 3x8 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…

A: Ans: Given a 3×8 matrix has a rank 3. We want to find the dimension of the null space, dimension of…

Q: Show that the inverse of a unit lower triangular matrix L will always be unit lower triangular by…

A: Consider a 2×2 unit lower triangular matrix as follows:            L=10a1 Let L-1=efgh. Therefore:…

Q: Prove that the product of two upper triangular matrices is always another upper triangular matrix.

A: We have to prove that the product of two upper triangular matrices is always another upper…

Q: Find a family of the matrices that is similar to the matrix

A:

Q: and B are square matrices with dimension 2 x 2, C is a matrix with 5 columns. What should be the…

A: Matrix CD is square matrix because A is square matrix.  And CD is define if column in C is equal to…

Q: 2. Every square matrix A can be decomposed as a product of three matrices A = SDR where S and R are…

A: We shall give an counter example for part (2)

Q: Suppose A = QR is a QR factorization of an m × n matrix A (with linearly independent columns).…

A:

Q: Suppose A is a 3x3 matrix. Let B be the matrix obtained from A by performing the following…

A:

Q: If matrix A (mxn) has full rank, and I multiply it by its conjugate transpose A*. In other words,…

A: We will give a counter example that will prove this statement wrong.

Q: Prove that the LU factorization is unique by considering the possibility that LU = LŨ, for some L, L…

A: The solution is given as

Q: Suppose A is a symmetric n × n matrix and B is any n × m matrix. Show that BTAB, BTB, and BBT are…

A:

Q: An mxn upper triangular matrix is one whose entries below the main diagonal are zeros, as is shown…

A: The solution is given as

Q: Which of the following matrices is positive definite?

A:

Q: Suppose that A and B are square matrices with the property AB = BA. Show that ABn = BnA for every…

A:

Q: Prove that if both products AB and BA are defined, then AB and BA are square matrices. Assume that A…

A: AB and BA are both defined.

Q: find the set of all 2X2 stochatic matriceswith elements that are either 0 or 1

A:

Q: If A and B are invertible 2 × 2 matrices with nonnegative entries, then A + B must also be…

A: Let's take one counter example of the given conditions. That is A and B are invertible 2*2 matrices…

Q: If A, B are two n x n orthogonal matrices, then AB is also an orthogonal matrix. True False

A: Give:  If A , B are two n×n orthogonal matrices. To check: product of matrices A and B are…

Q: Prove that the sum and the product of two lower- (upper-) triangular matrices is lower- (upper-)…

A: Topic:- matrix

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.