3) Let A = 2 -1 Find a matrix P that orthogonally diagonalizes A. Use P to com- 0 -1 pute A5.

Q: Construct a 3 x 3 triangular matrix A so that 1] the vector 2 is in Col A. 3]

A: We know every lower or upper traingular matrix is a triangular matrix.

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: and = %3D are oignualus of a matrix A Corraspondeng to the egnualuong=2 and >=-2 then = ACTa t Ja)=…

A: For a given matrix A if 'x' is eigen vector of matrix A corresponding to the eigen value ' q ' then…

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

A:

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

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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: Show that if A is an upper triangular matrix, then A T is lower triangular.

A: A is an upper triangular matrix. That is, Now let A=aij be a n×n upper triangular matrix. Then,…

Q: Let A be square matrix. If A" = 0. A= Oava %3D for n> 2. Then

A:

Q: Suppose that Q is an orthogonal matrix, then O a lQ°| = 4 O b. Q°| = 2 O d. Q°| = 0

A: This question is related to Linear Algebra

Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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

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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: Is it true or false? If A is nxn matrix, c is scalar, then cA |=c | A| Birini seçin:

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Q: Find the matrix C such that BC = AT

A: Let A be an n×n matrix, Then the transpose matrix of A is also an n×n matrix denoted by AT. Now,…

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

A: Matrix A is said to be non singular if the determinant value is non zero.

Q: let A nonsingular matrix, c #0, c scalar (cA)" = CA -1 -1 %3D Select one: True O False

A:

Q: Construct a 3 x3 nonzero matrix A such that the vector is a solution of Ax = 0. 1 LA =

A: x=-1-1  1 Now let A=abcdefghi be the required vector. Then, Ax=0⇒abcdefghi-1-1  1=000⇒-a-b+c-d-e+f…

Q: Let A be a m times nm×n matrix such that Ax​=b and Ax​=c each have a solution for some choice of b…

A: Let A be an m×n matrix such that Ax​=b and Ax​=c each have a solution for some choice of b and c in…

Q: * Let A be and m x n matrix. Describe the matrix E such that EA is A with row swapped.

A: Given matrix A is a m×n matrix. And the elementary matrix E and EA are row swapped. Since elementary…

Q: Find three values of c for which the matrix C is not invertible.

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Q: Solve for the values of x and y using LU Decomposition from the given matrix and prove that PA-LU or…

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Q: Г1 3 2 5 1 [3 4 2

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Q: If A is an invertible n X n matrix, show that adj A is also invertible

A: Given: To Prove: Concept: 1. 2.

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

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Q: Find the standard matrix for the linear operator T: R^3 --> R^3 that first rotates a vector…

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Q: Determine whether the matrix is orthogonally diagonalizable.

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

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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: If a matrix A E Mn(R) and rank(A) = n, is it true that the column vectors of A are linearly…

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Q: Find a (2x2) singular matrix A that maps (s1, ss) into (s2, s6).

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

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Q: Let A = UEVT be a SVD of a square matrix A. What is the product of the diagonal elements of E, in…

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Q: Find Q and R in the matrix factorization 3 2 4 1 -1 QR. %3D [0 0 As usual, Q is an orthogonal matrix…

A: Given

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

A: For a nonsingular matrix A and nonzero scalar K To show that kA-1=1kA-1 Consider a non singular…

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: Find a matrix P that diagonalizes 1 0 0

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Q: Find h and k, consistent: which makes matrix Gud Suo = k

A: We have to find the values of h and k for which the given system is consistent.…

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

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Q: Determine the matrix C such that (CT – 21) 1 1 2 2 3

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Q: Given the matrix 6 0 0 A= 0 2 2 0 2 2 find an orthogonal diagonalization of A: A = QDQ"

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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: Find a matrix P that orthogonally diagonalizes A, and determine P-'AP. A = 1 4 P = P = 2 V3 V3 2 P =…

A: First we need to find eigen values:

Q: Let Q be an orthogonal matrix such that QA makes sense.                          Show that (QA)+ =…

A: Given, A be a matrix and Q be an orthogonal matrix such that QA makes sense. We have to use product…

Q: Show that if A is an orthogonal matrix, then AT is also orthogonal.

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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: [5 Let B =E dl: Is the matrix B orthogonally diagonalizable? If yes, find a diagonal matrix 2 0…

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Q: let A be an mxn matrix and v and w vectors in Rn. If v and w were both solutions to Ax=0, show that…

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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