Let A = XYT, where X is an m × r matrix, YT is an r × n matrix, and XTX and YTY are both nonsingular. Show that the matrix B = Y(YTY)−1(XTX)−1XT satisfies the Penrose conditions and hence must equal A+. Thus A+ can be determined from any factorization of this form.

Q: Suppose A is n x n invertible matrix ( AA-1 = I), then the first column of A-1 is orthogonal to the…

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Q: Let A be 2 x 2 matrix, if the matrix B results from A by adding 3 times the first row of A to the…

A: The objective is to find out the correct option.

Q: Give the matrix X such that -1 -1 3. -2 X = 0. -5 Type DNE 4. -5 1 0. 0. if such a matrix does not…

A: Given: 02-135-2-3-51X=-1000-50004 If AX=B, then X= A-1B. We know that A-1=adjAA and adjA= cofaijT

Q: For a nonsingular matrix A and a nonnegative integer p, show that (Ap)−1 = (A−1)p.

A: The objective is to show that AP-1=A-1P for a non singular matrix A and a non negative integer P

Q: For each of the following matrices A, determine its reduced echelon form and give the general…

A: SO we will convert these matrix into echelon form by row operation . And than we can find solution…

Q: Find the symmetric matrix A associated with the given quadratic form.…

A: Solution: Consider the given quadratic form is: 2x2 - 3y2 + z2 - 4xz we know that if ϕ =…

Q: Find conditions on a, b, c, and d such that B = as attached commutes with every 2X2 matrix

A: B=abcd Let A=uvxw BA=au+bxav+bwcu+dxcv+dwAB=ua+vcub+vdxa+wcxb+wd Let BA=AB…

Q: Let X and B be matrices. If we have that B is a symmetric matrix (B is equal to its transposed…

A: Symmetric matrix are those matrix whose transpose is equal to the matrix. Invertible matrix are…

Q: For which value of x is the following matrix not invertible: 1 1 3x A = 3x 3x 3x 3x 3x O 2 4 O1/3 1

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Q: Let A = C 1. and X be a matrix satisfying: 2XT-A = (X + 2B)". B Then X is equal to the above equal…

A: The given problem is to find the matrix X which satisfies given matrix equation with given matrices.…

Q: Let A 1B = 5 l, and C-1 = If X is a matrix that satisfies: %3D %3D 2B = Al2 - XC then X is

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Q: Let X be the 3 x 3 matrix such that left-multiplication by X has the same effect as applying the…

A: In this question we have to find the (1, 2) entry of x.

Q: Create a 5 x 3 matrix, call it A, with no more than 3 zeros such that the columns of A are linearly…

A: Let us consider a matrix A=-4-300-14103546-7-3-9 First we will show that columns of matrix are…

Q: 3. Find x such that the matrix A is equal to its own inverse. A = G %3D

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Q: For each of the following matrices A with entries from R, find a diagonalmatrix D and an invertible…

A: Given the matrix  A=1332

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

A: Given matrix, 210112021

Q: Let A be an m x n matrix, and let B be an n x m matrix. Show that if m > n, then AB is not…

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Q: If A is an nxn matrix and B is obtained from A by performing the following elementary row operations…

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Q: 2 Consider the 3 x 3 matrix B = 1 2h -1 1 1

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Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

A: Given:0111 over ℤ2

Q: Show that if C and D are n×n row equivalent matrices, and Cx=0 has a non-trivial solution x !=0,…

A: Given that C and D are row equivalent matrices such that the system Cx=0 has a non trivial solution…

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

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Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 1 -1 A =0…

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Q: Verify by finding the matrix of S 0 T (a) by direct substitution and (b) by matrix multiplication of…

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Q: Let p(x) = x³ – 2x + 4 and compute p(A). |2 A = |0 -3 4 NOTE: Write the elements of the matrix…

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Q: For the matrix A, find (if possible) a nonsingular matrix P such that PAP is diagonal. (If not…

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Q: ^ = [1 ] A If A is diagonalizable, find an invertible 2 x 2 matrix P and a 2 x 2 diagonal matrix D…

A: Given that the matrix A=0-440. If the given matrix is diagonalizable , find an invertible matrix and…

Q: Let A be an m x n matrix, and let b1,..., bk be vectors in R" such that the system b; has a solution…

A: This question related to linear algebra's topic linearly independent set.

Q: For a nonsingular matrix A and nonzero scalar k, show that (k A)−1 = 1 k A−1.

A: Given that A is nonsingular matrix. That is, A≠0. Since k is a non zero scalar, kA≠0. Therefore, kA…

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

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Q: Suppose A is a 2 × 2 matrix, where -2 | u = Au = -4 A?u = 4 A³u 2 20 – 20 – 10. The minimal…

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Q: Give an example of a matrix A such that (1) Ax = b has a solution for infinitely many b e R°, but…

A: If  the dimension of the column space of  A will be 3  (or if A has set of three linearly…

Q: Let A be the matrix Find p(A). p(x) = x' - 2r + 4

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Q: Show that for any n x n matrix A there exists another n x n matrix M such that MAM-1 = AT, where AT…

A: Consider the given information. Let the matrix A is an n×n matrix and M is a m×m matrix. And the…

Q: Let A be a symmetric 2 X 2 matrix and let k be a scalar. Prove that the graph of the quadratic…

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Q: If A is m x n matrix and Ar b has no solution for some b, then %3D

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Q: 2. Write the quadratic function f(x,,y;)=-3x; +2x,x, – 3x; – 4x, – 4x, +6 in matrix form as f(x) =…

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Q: Show that if an n × n matrix A is positive definite, then there exists a positive definite matrix B…

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Q: Let A be a nilpotent matrix (that is, Am = 0 for some m > 1). Prove that if A is diagonalizable,…

A: Consider a nilpotent matrix A. So Am=0 for some m>1.

Q: Suppose that A is an n × n matrix satisfying the equation A4 + 2A2 − 3A − I = O , where I is the…

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Q: For matrix A if f(X) = X2 + 4, what is the answer to f(A)?

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Q: Let A, B, C be n × n matrices and assume that A is invertible. Solve the equation A(B + X) = C for…

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Q: If A is a 2 x2 matrix such that det A) = - 3 and tr(A) =5 then the characterestic polynomial of A is…

A: The characteristic polynomial is, p(λ) = λ² - (tr A) λ + (det A)  Given, det(A) = -3 and tr(A) = 5

Q: Let A be a 4x4 matrix and det(A)=2. Find det(2A-)'

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Q: Find c such that the number of the pivots to the matrix below is 2: 1 1 1 -1

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Q: Let A be a 3 x 3 matrix such that det(A) = 12. Suppose B is obtained from A by applying the…

A: We have to find the  det(B).

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

A: Given a matrix, Let A=0111 over Z2 To find the inverse of A.

Q: For A e Mnxn(C), the function ||A||. = max1<ijśn |aij| is a norm on Mnxn(C) but not a matrix norm.…

A: Matrix Norm: Let Mn×n(ℂ) be the vector space of all matrices of order n with entries in the field ℂ,…