Matrix A is equivalent to matrix B, written A B, if there exist nonsingular matrices P and Q such that B = PAQ. Prove that z is an equivalence relation; that is, (a) AzA, (b) If A z B, then BzA, (c) If A z B and Bz C, then A C.

Q: Let A and B be two invertible matrices of the same size. Which of the following is false: If A is…

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Q: Show that if A is a symmetric matrix, then AT is symmetric.

A: we have to show that if A is a symmetric matrix, then AT is symmetric.   as we know that a matrix B…

Q: Determine whether V and W are isomorphic. If they are, give an explicit isomorphism T: V--->W. V…

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Q: How is the matrix of R^−1 obtained from that of R in general, that is, when A = {a1, . . . , am}, B…

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Q: Let A and B be 5x5 matrices such that det(A) = 4 and det(B) = 3. %3D Compute det(2B)"(AB)")

A: We have to find

Q: Prove that if an n × n matrix A is not invertible, then A[adj(A)] is the zero matrix.

A: 1). Matrix A is invertible if and only if matrix A is a non singular matrix. That is, determinant of…

Q: Let A be an m ×n matrix and B be an n ×p matrix. Prove that AB can be written as a sum of n matrices…

A: Given that A be a mxn matrix and B be a nxp matrix.Now, prove that AB can be written as a sum of n…

Q: A and B are n X n matrices If Bis invertible, prove that det(B-1AB) = det(A)

A: A and B are n X n matrices and B is invertible.

Q: If A and B are arbitrary real m X n matrices, then the mapping (A, B) = trace(A" B) defines an inner…

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Q: Show that if A is a nonsingular matrix, then adj A is non- singular and 1 (adj A)- = A = adj(A-).…

A: Given: A is a nonsingular matrix. Since A≠0

Q: If A is a symmetric matrix, then AT =

A: If  A is symmetric matrix then AT is also symmetric matrix

Q: Prove that if A is a symmetric matrix, then adj A is sym- metric.

A: To Determine:Prove that if A is a symmetric matrix, then adj A is symmetric. that is (adj A)T=(adj…

Q: Suppose P = QAQ-1 where Q is orthogonal, and A is upper triangular. Prove that if P is symmetric,…

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Q: Prove that if A is an 2021 x 2021 skew-symmetric matrix, then A must be a non-invertible matrix.

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Q: Prove that if A is a nonsingular upper triangular matrix, then A−1 is upper triangular.

A: we have that A is a nonsingular upper triangular matrix and A-1 be its inverse.

Q: [:] Suppose A is a 2×3 matrix such that A and A -3 Compute the product A

A: I have writen the vectors in linear combination of given two vectors and applied A in both sides

Q: By induction, prove that if A1, A2, ••• , An are invertible matrices of the same size, then the…

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Q: Prove that if A and Bare symmetric n X n matrices, then so is A + B

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Q: Let A be a m × n matrix with columns c1, …, cn. Prove that {c1, …, cn} is independent if and only if…

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Q: Let Q be a orthogonal matrix prove that If Q1 and Q2 are orthogonal n X n matrices, then so is Q1…

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Q: Prove that B is row equivalent to A if and only if there exists a nonsingular matrix M such that B =…

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Q: If A and B are matrices such that AB is defined, then it is true that (AB)T = ATBT %3D True False

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Q: 2. If in the general state(x, Ax) = (x, Bx be for each x at Euclidean space, then B = A is not…

A: A matrix is symmetric when the matrix equals to its transpose. When a matrix equals negative of its…

Q: If both matrices A,B are orthogonal prove that (ab) is also orthogonal

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Q: Let A be an n × n matrix. Prove that if Ax = 0 for all n × 1 matrices x, then A = O .

A: we have been given that Ax = 0 for all n × 1 matrix x and  A be an n × n matrix.

Q: If A is diagonalizable such that A= XDX-!, then the diagonalizing matrix X is unique. Select one: O…

A: Given that A is diagonalizable and A=XDX-1 Now, the matrix X is formed by the eigen vectors of the…

Q: Matrix A is equivalent to matrix B, written A z B, if there exist nonsingular matrices P and Q such…

A:

Q: Let A be a square matrix such that A2 = 0. Prove that (Af)2 = 0

A: Given that A is a square matrix and A2=0. In order to prove (At)2=0 following theorem are used.…

Q: snip

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Q: Prove that if A is a symmetric matrix, then adj A is symmetric

A: Let A be A symmetric matrix.

Q: Let A € RPXm have rank r. Show that there are matrices C and B such that A = св, where C E RPXT and…

A: Please check the solution in next step

Q: Show that if A is an orthogonal matrix, then det(A) = +1.

A: To prove, detA=±1

Q: Let A = {a, b, c, d} and let R and S be the relations on A whose matrices are (1 0 1 0) 1 0 0 1 1 0…

A: The set is A = {a, b, c, d}. The matrices representing the relations R and S, respectively, are as…

Q: Let A be a m x n matrix, U be a p × m matrix and V be an x p matrix such that VUA= In,where I, is…

A: A square matrix is invertible if and only if the determinant is not equal to zero. Which means ATA…

Q: IF A is diagonalizable such that A XDX, then the diagonalizing matrix X is unique. %3D Select one: O…

A: Given A is diagonalisable and A = XDX-1

Q: Let A € RPXm have rank r. Show that there are matrices C and B such that A = CB, where C e RPxr and…

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Q: (a) Prove that if A and B are symmetric n X n matrices, then so is A + B. (b) Prove that if A is a…

A: Part-(a) : Given : A and B are symmetric n×n matrices. We have to prove that A + B is symmetric n×n…

Q: Prove that A+ A' is a symmetric matrix, w

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Q: Show that is A is a square matrix, then A + AT is a symmetric matrix. You can use any matrix for A…

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Q: 6. Show that (AA)* = X* A* for all A E C and all matrices A.

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Q: Let A be an m x n matrix. Prove that if n is an odd number, then rank(A) = nullity(A).

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Q: Let H: R* → R2 be defined by H(x, x2, X3, X4) = (x3 + x4, X1). Find the standard matrix for H. (H is…

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Q: Prove that |A|=|AT|. Recall, that if A=[aij] and its transpose is AT=B=[bij], then bij=ai

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Q: show that if At exists for matrix A > then A is to

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Q: If A is an n x n symmetric matrix and B is any n x n invertible matrix, prove that A is positive…

A: Consider the given conditions. The A = n × n symmetric matrix and B = n × n invertible matrix.…

Q: Let A and B be n×n matrices. Prove that the productAB is nonsingular if and only if A and B are…

A: Definition:  A matrix is said to be non-singular if its determinant value is non-zero. It is given…

Q: Prove that if A is an orthogonal matrix, then ∣A∣ = ±1.

A: Given: A is orthogonal matrix   To Show: A=±1

Q: Prove that if ∣A∣ = ∣B∣ ≠ 0, and A and B are of the same size, then there exists a matrix C such…

A: we have |A|=|B|≠0   A and B are of the same size    We have to prove |C|= and A=CB

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.