Let -1 9 -1 1 1 2 0 |and P =| 0 0 1 1 0 5 A = 1 %3D 0 15 -2 Given that P diagonalizes A, then compute A". -1 -4104 1 -10245 1

Q: 4. Let A = . Show that A can be diagonalised. Then, compute Aº.

A: Given that

Q: Find a 3 x 3 matrix A such that Ax = 9x for all x in R3. A II

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Q: Let 1 5-1 A = 0 1 0 and P = 0 0 0 15-2 05 Given that P diagonalizes A, then compute A¹¹. i A" i i

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Q: A matrix Q ∈Mn×n(R) is called orthogonal if QQt= I. Prove that if Q is orthogonal, then det(Q) = ±1.

A: The determinant of the product of the matrices is the product of the determinant of the matrices.

Q: 3 0 Find a matrix P such that P- 30 2 1 1 0 O A. P= 1 1 - -1 0 O B. P 1 1 1 -1 C.P = 0 1 1 0 O D.P 1…

A: P-13021P=3001 From the given that P-1AP is diagonal matrix A=3021 We need to find the eigenvectors…

Q: Let A be an 7 × 7 matrix in which every entry is 1 and I7 be the 7 × 7 identity matrix. Prove that…

A: Matrix 'A' is  defined such a way that , all the entries are 1 of order 7×7. Some results: If sum…

Q: Let A be an n x n matrix. Prove that det(A*) = det(A).

A: Given:

Q: 2. Let n x n matrix A have the form Au Azz A = where An is k x k (where k < n). Show that A is…

A: The given matrix is  A1100A22 A matrix is called non-sigular if the value of its determinant is…

Q: Given that the singular value decomposition of 2 3 A is given by the matrices 2 -1 U = V5 (1 2 1 -2…

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Q: |2 1. (exercise 3.1.18) Let A = 6 3 Find 2 x 2 matrices B and C such %3D that AB = AC but B # C.

A: Given matrix A=2163

Q: -1 2 Let A = 2 1 5. b = -4 1 2 4 The orthogonal projection of b onto Col A and the least-squares…

A: None of given answer is correct. But most nearly Option b is correct. Choose Option (b)

Q: Let K be an nxn matrix over Z26 such that K = K-1. Explain why either det(K) = 1 or %3D det (K) =…

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Q: -1 21 1 2 Show that A = 2 2. is diagonalizable by finding P and D such that P-'AP=D for a diagonal…

A: The matrix A can be diagonalized if there exists an invertible matrix P and diagonal matrix D such…

Q: (BH) Consider the following matrix in R5×5. * 0 0 0 0 0 0 0 0 0 * A = * * * where the *s are…

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Q: Prove the formula for a nonsingular n × n matrix A. Assume n ≥ 2.∣adj(A)∣ = ∣A∣n−1

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Q: Let n > 2 and let A be an n xn matrix. Prove that "det(adj A) = det(A)"-1."

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Q: Pls explain to me step by stepThanks

A: The given matrix is

Q: 0 1 0 0 0 1 and X= 2/3 0 1/3 a. Show that XP = X. 3x3 1x3 [11:3/2] x [i] = [ (09 - 160 - 32 1/3 X -…

A: Given  P=01000123013 and X=1132

Q: [1 2 a-lf A = 0 1 -1 lo o 4 prove that (A - AT) is askew-symmetric 2 matrix

A: simple sunstract A minus transpose A and see that property of skew symmertic matrix is follows.

Q: 3 1 -4 1 -3 A = -1 & & B = Find ??? 1- Prove that At + Bt + Ct = (A +B + C)t %3D 2- Prove that (B *…

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Q: Show that if A is an n x n matrix, then A" can be written as a linear combination of the matrices I,…

A: Cayley-Hamilton Theorem:- Every square matrix satisfies its own characteristic equation.

Q: Let A and B be n x n matrices such that AB=In. Prove A=B-1 (and hence B=   A-1).

A: Given: -

Q: 5. Let A -1 2 1. Express the matrice A as the product of elementary matrices. 3 1

A: We have to express the matrix as the product of elementary matrices.

Q: O Consider a non-singular n x n matrix A. Let A = inf{||SA|| : A+ 8A is singular}. Show that 1 A…

A: We are given a non-singular n×n matrix A and ∆ = inf{||δA|| : A+δA is singular} And we have to show…

Q: Show that the characteristic equation of a 2 × 2 matrix A can be expressed as 1² – tr(A)A + det(A) =…

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Q: Consider the following Gaussian elimination: Г18 —3 O 0] [1 0 0] -7 -7 → 18 -3 1 1 01 1 1 + 18 -3 0…

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Q: 4. For the matrix 1 X' = 1 1 1 4 -2 3 -5 compute P = X(X'X)-1X' and M =I- P (a) Verify that MP = (0.…

A: Consider the provided matrix, X'=11114-23-5For to find P=XX'X-1X' ,X=14 1-2 13 1-5

Q: 3. Let A = aij be an n x n upper triangular matrix. (a) Prove that det(A) = a11@22 ann. (b) Prove…

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Q: A. modrix g 1 - V fo " Kariky hdher de matrix の det A- 2.

A: For part (i) of a: According to the given information, it is required to calculate the determinant…

Q: Let A and C be n×n matrices such that ​CA=I​ (the n×n identity​ matrix). Show that Ax​=0 has only…

A: Here, CA=I, where I is the identity matrix.

Q: 4. Let M (for matrices) be the set of all 2 x 2 matrices over the reals and x, y ∈AM. Does…

A: This statement is not true.

Q: a *15. Given a = 6ER°, define T: R³ → R³ by T (x) = a x x. Prove that T is a linear trans- formation…

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Q: A and B are n X n matrices Prove that det(AB) = det(BA)

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Q: What is the det(A) if a matrix has p(A)=13 - 212 -A +3 as its characteristic polynomial. O A. -2 В.…

A: Proceed as shown below...

Q: Recall the Vandermonde matrix X given in (3.1.3), and define 1 V,(x) det 1 %3D Xn-1 Xn-1 n-1 1 Show…

A: As per the question we have to prove the given recurrence relation of the nth order Vandermonde…

Q: |-1 7 -1 Let A= 0 11 1 1. and P= 0 0 1. Given that P diagonalizes A, Compute A11. 1 15 -21 101

A: We have to find A ^11

Q: Let 1 = [3 13 31 orthogonal matrix P so that PT AP is a diagonal matrix (r from distinct igor n A

A: In this question, the concept of Eigenvalues is applied. Eigenvalues Eigenvalues are a unique set of…

Q: (a) A matrix B in Mnxn(R) is called orthogonal if BB' = I. Prove that if B is orthogonal, then…

A: Note:As per our honor code, we will solve first sub-part for you. To get remaining sub-part solved…

Q: 6.* Suppose that A = [aj] is a 3 x 3 matrix whose entries are equal to either 0, 1, or 2, namely aij…

A: The given matrix is A=aij of order 3×3 whose entries are equal to either 0, 1 or 2. i.e. aij∈0,1,2 ∀…

Q: A matrix Q ϵ Mnxn(R ) is called orthogonal if QQt = I . Prove that if Q is orthogonal, then det(Q) =…

A: Given data: The orthogonal matrix is given by "Q". The given condition is  QQT = I.....(1) Now, take…

Q: Consider the matrix 3 0 - 2 A = 1 1 - 5 2 - 1 | d] Find the Condition Number K(A) USING INFINITY…

A: The condition number of a matrix, which is invertible, is defined as…

Q: Let A be a 4 × 4 matrix and let x1, X2, X3, X4 be given by -183 -46 139 49 -93 -23 71 25 X1 = X2 =…

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Q: 2. Compute the matrices D, P such that D =P-'AP. Verify the equation holds. [7 5 0 A 1 0 1

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Q: 1 a. Verify that A? = I when A 101 -8 b. Use partitioned matrices to show that M² = I when 0 0 0 0 2…

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Q: 7. Prove that there is no 3 x 3 matrix A with 01 1 0 0 1 0 0 0 1 1 0 and A 100 %3D 0 00

A: In this question, concept of matrix is applied. Matrix A matrix is a rectangular array or table in…

Q: Consider the following Gauss-Jordan reduction: 1 9. 5 1 1 1 0. 1 -2 0. -2 5 1 0. = 1 1 1 1 A Ej A E2…

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Q: Let A be the n × n matrix given by Show that det (A) = (a - 1) n − 1(a + n - 1)

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