--[i 1. (a) Let A = 1-3 Find all 2×2 matrices B which satisfy the relation AB = BA.

Q: Let G be a 2x2 matrix with a and b in the top row and 0 and c as the bottom row, where a,b,c are…

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Q: aj bị c1 adjA if A = |a2 b2 c2| is a non-singular matrix prove that A: detA аз b3 C3

A: Matrix A is a non-singular matrix. This means; det A ≠ 0    A =a1b1c1a2b2c2a3b3c3adj A…

Q: [2a11 5a12 Let A = |2a21 5a2 -3a23 2a31 5a32 -3a33 diagonal matrix and neither B or D is equal to…

A: The given matrix isA=2a115a12-3a132a215a22-3a232a315a32-3a33.We have to factorise A into A=BD where…

Q: Let A and B be two square matrices of the same size. Prove that det(AB) = det(BA).

A: Using Determinant and elementary row operations,

Q: Determine x if: [2х 4] + %3D 5

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Q: 2. Find the conjugate and tranjugate of each of the following matrices: a) - 5 - j 22 j3 j4 3 4 1 +…

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Q: 1 Find the linear combination 2$1 +382 + 4s3 b. Then write b as a matrix-vector multiplication Sx.…

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Q: () Write the statement of Cayley-Hamilton theorem for square matrices.

A: Cayley-Hamilton statement

Q: Let A 1 2 −1 -2 3 -2 -1 1 1 Diagonalize A to find A100.

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Q: Let A = (a) and B = (A + B)(A + B) (b) A2 + 2AB + B² 3) Let A2 and B2 denote the matrix products AA…

A: A=5423B=8759

Q: a) If A and B are invertible and their inverses are A¹ and B-¹ respectively, prove that the inverse…

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Q: Find elementary matrices e and e2 such that di 0 e2 = 1 5 1 5 e1 0 dz) for some numbers d and d2.

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Q: Use the definition of Ax to write the vector equation as a matrix equation. X1 7 2 - 8 -5 + X2 - 3 9…

A: I am going to solve the problem by using some simple algebra to get the required result of the given…

Q: Q2) In each of the following cases, find the matrix A for which [v]D=A[v]B a. B={1, 2x, 4x²-1} and…

A: Here we use the definition of the change of basis matrix. For that we first write the basis elements…

Q: 6 -1 Evaluate ABT – 3C given that (2 -2 lo -1 2. -2 A = 6 -3 ‚B = and C = -12 7. 3. Use matrix…

A: To solve the given matrix problems.

Q: [121] In other words, write A = SDS-¹ = SDSt where D is a diagonal matrix and S is an isome- try.…

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Q: Let W be the set of all vectors of the form [3s 4r5t] 2r + 2s - t 3s - r + 5t 3r + 2s + 4t with r, s…

A: The set ( W ) consists of vectors that can be formed by linear combinations of the vectors with…

Q: Folve differential equation by variation of parameters. y" – 4y' + 4y = 2e2

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Q: [2 Let A = Find all matrices of the form B = that commute with A. P In other words find all matrices…

A: We have to do both the matrix multiplication.

Q: Consider the matrices, 1 i V1 – 6² 0 -6 A = 1 а 1 B = 1 1 0 V1– 62 a where a and b are real…

A: Given, the matrices                              A=a1i1a1-i1a and B=1-b20-b010b01-b2 Then, we have…

Q: a. Which of the matrices are orthogonal (has orthonormal columns)? V3 -2 V2 V3 [1 1 -4] -2 1 Find…

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Q: Prove that An nxn matrix A is non singular if and only if it can be written as a product of…

A: We prove that an nxn matrix A is non singular if and only if it can be written as a product of…

Q: Let A be an m x n matrix and let b and c be column vectors with n components. Express the dot…

A: Answer :

Q: Let W be the set of all vectors of the form with r, s and treal. Find a matrix A such that W =…

A: Solution:-

Q: a) Find bases for the Row space, Column space and Null space of A. b) Find the rank and the nullity…

A: A matrix being in row echelon form means that Gaussian elimination has operated on the rows, and…

Q: 3.) Find the inverse matrix? 2 Use the adjugate of A = 0 -2 1 to find A-1 | 1 0 0 - 2 3.

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Q: Let A and B be the matrices as shown. '1 2 1 1 2 1 ^ - ( ²³ ) ·- - 6 ÷ ³) A = 0 5 1 B = 2 -1 4 2 −1…

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Q: b) 0 0 j5 - 1 6 5 + j6 j8 j8 j4 3 - j 7 0 j2 j2

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Q: real matrix which is not diagonal. If (A + I)² = 0,

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