If M AM is a symmetric matrix and M is 5x4 matrix then O a. A is orthogonas O b. A is invertible O c.A is skew-symmetric O d. A is symmetric

Q: Show that if A is any m × n matrix, then Im A = A and AIn = A.

A: We know that if A is a matrix of order m x n and B is another matrix of order n x p, then their…

Q: Let C and D be n x n skew-symmetric matrices. Prove that if CD = – -DC, then CD is a skew-symmetric…

A: Given problem:- Let C and D be n x n skew-symmetric matrices. Prove that if CD=-DC, then CD is a…

Q: If an m x n matrix U has orthonormal columns, then UTU = I.

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Q: if A is (m*n) matrix, prove 'rank(A)=n-dim(N(A))

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Q: Suppose that A is an n x n matrix such that A² = 0. a) Show that if 7 E im(A), then 7 € null(A). (In…

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Q: Given the partitioned matrix A = [ B]. B]₁ C D in which B and C are invertible. Which of the…

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Q: Prove that if A is an n × n matrix, then A − AT is skew-symmetric.

A: Let  A be an n × n matrix, To prove : A-AT is skew-symmetric, that is (A-AT)T=-(A − AT)

Q: If A is an n×n matrix with Col A​ = Rn​, how many solutions will there be to Ax​=b​, for any b in…

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Q: Let A be an m × n matrix. Show that A is row equivalent to O if and only if A = O .

A: Consider the given information as A be an n×nmatrix

Q: Let C be a nonsymmetric n × n matrix. For each ofthe following, determine whether the given…

A: Given  B=C-CT Find transpose.

Q: If A is an m · n matrix where A· A is defined, and k e N, recursively define A*

A: If A is a m × n matrix where A • A is defined and k lies in N then we have to recursively define Ak…

Q: If P is an n x n matrix with orthogonal columns, then PT = P-1 Select one: True False

A: Let P be the given orthogonal matrix

Q: Are the fOllowing statem ue of faise? Justify with a e) or a counterexample (if false). (a) For any…

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

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Q: 2. find a matrix P that diagonalizes A, and compute p-AP. [500] Го о о A= 150 015 000 301

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Q: If A is an m x n matrix then A' A and A have the same rank. true false

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Q: Suppose that A is an m × n matrix and satisfies the following conditions: dim(row(A)) = 3…

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Q: In our course, you may have noticed that we mainly talked about orthogonally diagonalizing a matrix…

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Q: An n*n matrix C is said to be symmetric if C Select one: True O False

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Q: If A is an n xn matrix then det(A)=Ddet(-A). Select one: O True O False

A: Introduction:- Statement -> if A is square matrix of order n X n, then det(kA) = kn det(A)

Q: If the null space N(A) of a 5 xX 6 matrix A has dimension 4, what can you say about the dimension of…

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Q: If Q+A= A holds for every m×n matrix A, show that Q = 0mn.

A: Consider the given equation, Q=A+A   Now, subtract the matrix A from both side: Q+A-A = A -A As, A…

Q: Suppose A is a square matrix. Show (a) A+A" is symmetric, (b) A – A" is skew-symmetric, (c) A= B+ C,…

A: Sum of symmetric and skew-symmetric matrix is matrix it self. Like for matrix A, Symmetric matrix =…

Q: (a) Let A be an m × n matrix, and let B be the result of performing a single elementary row…

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Q: An n*n matrix C is said to be symmetric if C' = c Select one: True False

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Q: If A is a m × n matrix and B is a n × p matrix then AB is a m × p matrix. True or False

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Q: T An n*n matrix C is said to be symmetric if C = C Select one: O True O False

A: We have to check

Q: Prove that if A and B are n × n skew-symmetric matrices, then A + B is skew-symmetric.

A: Given: To Prove: Concept: 1. Transpose 2. Properties of Transpose:

Q: A matrix B in Mnxn (C) is called skew-symmetric if Bt= -B. Prove that if B ϵ Mnxn (C) is…

A: Let B be skew-symmetric matrix of order n, where n is odd, then we have

Q: For a matrix A having JA| = 0, which of the following are true? * O A- exists with |A¬' |= 0| O A-…

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Q: Suppose A is a skew-Hermitian matrix and Catib)A is alo ckew.Hermifian mabrig, then fa the valu of…

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Q: Given the following set S of matrices , find a matrix A in M2 2 so that SU{A} spans M2.2 and a…

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Q: If a is skew symmetric nxn matrix and n is odd,prove that det A = 0.

A: Consider a skew symmetric n x n matrix A where n is odd. Here the objective is to prove that det(A)…

Q: Show that if A is any m × n matrix, then Im A = A and A In = A.

A: Given: Matrix A of order m × n.

Q: Suppose that A is an invertible matrix with n columns, and entry aij in row i and column j. 1.…

A: Let matrix is A and the entries are aij .

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: 1. Suppose (B – C) D = 0, where B and C are m x n matrix and D is invertible. Show B = C

A: ( B - C )D = 0 where B and C are m × n matrix and D is invertible.  Then, we have to prove that B =…

Q: If A E Mpx, (C) nXn is a square matrix, and B is unitarily similar to А, then A and В have the same…

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

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Q: Suppose that A is a 3 x 12 matrix, and that 7(x) = Ax. If T is onto, then what is the dimension of…

A: We know that the null space of a matrix A of order n×m is the number of linearly independent…

Q: Prove that if A is an m x n matrix, B is an n x p matrix and C is a p x q matrix, then (AB)C= A(BC).

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Q: A matrix M ∈Mn×n(C) is called skew-symmetric if Mt= −M. Prove that if M is skew-symmetric and n is…

A: The matrix is not invertible if its determinant is 0.If k is multiplied to the matrix Anxn then,

Q: Show that if A is any n × n matrix, then (a) A + AT is symmetric. (b) A − AT is skew symmetric.

A: Symmetric matrix: Any matrix A is symmetric matrix if and only if it is equal to its transpose that…

Q: Given the matrix G =| 10 5 201 and d, = Then d, and d, are not G- conjugate if d, is given by -1.5]…

A: We know that Two vectors u and v in Rn are A-Conjugate for a matrix A of size n×n if  uTAv = 0…

Q: Suppose matrix A is m×n and B is n×p. Prove that if the columns of B are linearly dependent, then…

A: Let A be m by n matrix and B be a n by p matrix.

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

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Q: if A is a 5×8 matrix and Z is a 6×5 zero mat then A+Z=A Select one: True False

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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.