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

Q: (2) Determine all the real numbers a, b, c for which the matrix a 0 b 0 C is not diagonalizable.

A: The given problem is to determine for what values of a,b,c the matrix is not diagonalizable.

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: Write the dot product of (1, 4, 5) and (x, y, z) as a matrix multiplication Ax. The matrix A has one…

A: Given, A=145, x=xyz Ax=0

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: Express the linear function as F(x) = CX for some matrix C. f(x1,x2,x3,x4) = (5x3 - x1, 2x3 + x4,…

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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: Consider the following (real, symmetric) matrix: A-(10 40 = 40 158 Determine the real canonical form…

A: Given:  A=104040158 To find the real canonical form of a given matrix.

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: Let A be an m × n matrix and r, s E R two scalars. Show the property that (r + s)A = rA + sA.

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

A: To find matrix A such that

Q: 2 3 4 Let vi = 1 V2 = -2 V3 = 5, and E u = V2 3 Determine if u is in Col E, the column space of E.…

A: We have to determine u is in Col.E, the column space of E.

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: 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: f (x1,X2,x3) = xỉ + 3x1x2 – x2X3 +x3 – 4x3 Rewrite f in the matrix form x'Ax where A is a symmetric…

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Q: - Create a table that counts from 0-100 in intervals of 18. - Look at the tensor below 29 0 -51] G 0…

A: Since, you have posted multiple questions but according to guidelines we will solve first question…

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: a) Suppose that A and B are 4 x 4 matrices, det(A) = 2 and det((3ATB)-¹) = . Calculate det(B). b)…

A: As per our company guideline we are supposed to answer only one question kindly post remaining…

Q: Let -1 1 A = -1 1 -1 -3 3 Find an upper triangular matrix which is orthogonally similar to A.

A: An upper triangular matrix is a triangular matrix with all elements equal to below the main…