Let A be p x p matrix such that ATA = A². Show that: (a) tr (A - AT)" (A -A") =0. (b) Show that A is symmetric.

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: What is the Jacobian matrix J(xk) equal to?

A:

Q: Let A be an 3 x 4 matrix. What must c and d be if we define the linear transfor- mation T: R → Rd by…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: Find x such that the matrix A is equal to its own inverse.

A: We have A=-2-33x Now, A-1=1AadjA For a 2×2 matrix A=abcd, we have A=ad-bc  , adjA=d-b-ca Hence, for…

Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

Q: Let A be a matrix with singular values {1, 2, 3,..., 2022}. Find the singular values of the matrix…

A: Given,     A = [ 1, 2, 3, 4, . . . . . . , 2022]

Q: 4. Find the standard matrix for T where Ta2) =(2x,+x -2,).

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Q: Find x such that the matrix A is nonsingular.

A: Given: The inverse of a matrix is given as follows,

Q: Let A be an m x n matrix such that A"A is invertible. Show that the columns of A are linearly…

A:

Q: Let A be an n × n singular matrix. Then

A: if matrix A is singular that means its determined is zero.so at least one row of matrix A is…

Q: tet A be an mxn matrix Prove that on

A: Let A be an m×n matrix prove that Frobenis norm : AF=∑i=1m∑j=1naij212↔·2 on Cmn

Q: Let A = (a;;)ij be an m x n matrix of real numbers, and let f : R" -→ Rm be defined by x2 X2 f = A…

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Q: Now assume that f and g are both C2. Express the matrix of second derivatives V²F(x) in terms of f…

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Q: Let B be an invertible matrix. Show that A = BTB is positive definite.

A:

Q: Let A be an Hermitian matrix and let B = iA. Show that B is skew Hermitian.

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Q: Let A be an m × n matrix such that ATA is invertible. Show that the columns of A are linearly…

A:

Q: Compute det(Ei) if Ei is an elementary matrix of type i.

A: Elementary matrix is the type of matrix which is formed by changing one row of the identity matrix.

Q: If A is an m × n matrix of rank r, what are the dimensions of N(A) and N(AT )? Explain.

A:

Q: let B- 8. find a triangel ar matrix A such that

A: A triangular matrix is a type of square matrix. These are of two types:  Lower triangular  upper…

Q: Find the canonical form B and an invertible matrix P such that P−1AP = B.

A: In this question. we find the invertible matrix P and B such that P-1AP=B

Q: Let A be an m × n matrix of rank n and let P =A(ATA)−1AT . If b ∈ R(A)⊥, show that Pb = 0.

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Q: 2. Determine the matrix X, such that:

A: Solution:-

Q: Let A be p x p matrix such that ATA = A?. Show that: (a) tr (A - AT) (A- A") = 0. (b) Show that A is…

A: Let A be p×p matrix such that ATA=A2a) trA-ATTA-AT=0b) Show that A is symmertric

Q: Define what it means for a function Q : R" R to be a quadratic form. Furthermore, explain how we…

A: The quadratic form is one of the most important parts of linear algebra. Quadratic means degree two.…

Q: Compute the standard matrix for the linear map T : R² → R² which (1) rotates i by 0 = T, (2)…

A:

Q: Let A be 3 x3 R given matrix by over 2. A = -1 Using the result of A find the value (s) of makes the…

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Q: Find value(s) of ß for which the matrix A is singular. —3 - в |-2 B 1 1

A: Given:         A=β-3-β-2β1β10    A matrix is singular if and only if the determinant of a matrix is…

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 and B be n x n matrices.  Suppose that AB = On where On is a zero matrix of size n x n, and A…

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Q: Let A E Mn(C) denote the n x n matrix with all entries equal to 1. Show that A is positive…

A: Let A belongs to  Mn (C) denote the n x n matrix with all entries equal to 1. Show that A is…

Q: Find x such that the matrix is singular.

A:

Q: Find the QR-Decomposition of the matrix 1 4 0 0 7 0 36 Also, find || |l, of the above matrix.

A:

Q: Let A be a nxn square matrix having rank 2 then rank of (A^t A) is (A^t= Transpose of A)

A: Let A be a n×n square matrix and Rank (A) = 2

Q: hat is the matrix for

A: Given, consider the two-tank system shown below. Each of the two tanks contains 200 gallons of water…

Q: Let A = (ai;)ij be an m x n matrix of real numbers, and let f: R" → R™ be defined by 0-0 12 x2 = A f…

A: According to question, A = aijij Am×n matrix of real numbers,f : ℝn →ℝmf x1x2..xn = A x1x2..xn

Q: If the ows of a square matrix A are linearly dependent then A is singular

A: To determine whether the given statement is true or false.

Q: Let A be a 6 × 5 matrix. What must a and b be in order to define T : R“ → Rº by T(x) = Ax? Ах?

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Q: Verify that the matrix defines a linear function T that is one-to-one and onto.

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Q: Find a 2 × 1 matrix x with entries not all zero such that

A: Given: Ax=3x, where A=2112 let's assume matrix x is x=ab

Q: Find h and k, consistent: which makes matrix t. 6ud Sua = k |

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Q: Let A = (a;;)ij be an m x n matrix of real numbers, and let f : R" Rm be defined by 0-0 x2 x2 f = A

A: To find the derivative of f given: matrix A which has m rows and n columns  also the function f…

Q: Let A be a nondefective n × n matrix with diagonalizing matrix X. Show that the matrix Y = (X−1)T…

A:

Q: Let A be a nilpotent matrix of order n then A*n = 0 ) nxA = 0 A =nx1, l is Identity matrix

A: A be a nilpotent matrix of order n

Q: Show that if B is a symmetric nonsingular matrix, then B2 is positive definite.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Find x such that the matrix is singular.

A:

Q: If AC is an invertible matrix, then show that A is also an invertible matrix

A: Given- AC is an invertible matrix, i.e.- ACAC-1=I⇒ACA-1C-1=I⇒AA-1CC-1=I

Q: Find x such that the matrix is singular. A = -3 -6

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Q: Since it is, find the matrix P ^ -1 by using the adjoint matrix of the P matrix.

A: We are given that  We need to find the inverse of p-matrix

Q: Let A be an n xn Hermitian matrix and let æ be a vector in C". Show that if c= xAx, then c is real.

A:

Q: - L

A: Given that A=42-12 Take  A-λI=04-λ2-12-λ=0(4-λ)(2-λ)+2=08-6λ+λ2+2=0λ2-6λ+10=0λ=6±36-402λ=6±2i2λ=3±i