[13] Find a 2×2 matrix A other than the identity matrix for which A (r ר 75 7) -1 [][] 11 -1 1 1 -1

Q: 1. How would you verify that matrix A1 is the inverse of matrix A?

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Q: [5] Find three different 2 by 2 matrices that have A₁ = A₂ = 0.

A: Three different 2×2 matrices that have λ1=λ2=0 i.e, both eigen values are 0 are 0100,0020 and -4-284

Q: Q2] a) Write each (PRODUCT) of the following as a single matrix: i -17 2 -2 -1]-i -2 5] -2| -1 1 -1]…

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Q: the matrIX A into a product QDQ" where Q is orthogonal and D is diagonal.

A: Given,          A=-5-1-1-1-3-1-1-1-3

Q: Find the classical adjoint of the following matrices. -4 0 0 (b) (a) (A11 A12 A21 A22) (d) /3 6 7…

A: Hey since there are multiple subparts the first three is answered. If any particular subpart has to…

Q: Show that any 3 × 3 matrix of the form ⎧ ⎩ a 1 0 0 a 1 0 0 b ⎫ ⎭ is defective.

A: We have to show that given matrix is defective.

Q: [2 1 Q1 \a: find the inverse of the Matrix A= 1 1 2 1 -1

A: Given Matrix

Q: what value is in the 2nd row 2nd column of V x 3Q [3 4 -31 Г2 3 V = |0 -1 Q = 18 5 %3D 12 -2 1 1 5…

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Q: Let A and B be 3 × 3 matrices such that det (B) = -2 and 27 = det (-3AB A" B ²). 2 Find det(A).…

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Q: Find the following matrix product. Be careful to distinguish 2 x 2 matrices in the answers from 2 x…

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Q: (18) Does a 2 × 2 diagonal matrix commute with every other 2 × 2 matrix?

A: We have to check

Q: -3 -2 -3 17. Find the inverse of the matrix A= 5 3 5 2 1 1

A: Given A=-3-2-3535211 The inverse of A is given by A-1=1Aadj A A=-3(3-5)-(-2)(5-10)-3(5-6)…

Q: [2 -3 -47 The matrix product 2 4 [0 1 5 1

A: Given : 2-3-4015 . 3-12401

Q: <= [-5 1 is the product X = E₁ E₂E3 of elementary matrices E₁, E2, E3, find -5 35 E₁ = If x= 03-894…

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Q: Find the following matrix-vector product: [13 20 0 -1 3 -2

A: The given matrices

Q: Consider the following 3*3 matrix A=100,1-2-2,141 Show with your calculations that the matrix is…

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Q: Diagonalize A the matrix A. -27 2 3 4 3+ i√5 0 0 [S+W³² $ "VE] [3+1 0 3-i√√5 i√5] 0 0 [-³+1 0 O…

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Q: Find a 2 x 2 matrix such that (199-41 188- 6 6 2

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Q: [7 3 -5 Q1\ A- 1- if A = 0 4 and B= 3A;C = B+5I find matrix D such that 1 4 D= 2A+B-C

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Q: Is the matrix A invertible -1 2 3 -6 O True O False

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Q: Illustrate the Gersgorin theorem by the matrix 2 1+ 2i 0 A = -1 -2 – 2i 1/4 1/41/2 140 12 1/7 1/2…

A: We state the theorem and explain it with the help of the given matrix A.

Q: Find an explicit description of NulA by listing vectors that span the null space, where [1 5 -4 -3…

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Q: For this exercise assume that the matrices are all nxn. The statement in this exercise is an…

A: Given that if the equation Ax=0 has only the trivial solution then A is row equivalent to the n×n…

Q: Determine all the n × n− matrix A with the range such that A2 = A.

A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…

Q: Which of the following is the matrix C that satisfies the equality (CT +312) -1 3 (a) 2 -5 (:) 5 -2…

A: First take inverse on both sides of matrix equation CT+3I2-1=2714. CT+3I2-1=2714CT+3I2-1-1=2714-1…

Q: Calculate whether the given matrices are diagonalizable or not. That is, for each matrix, calculate…

A: We will use the fact if the eugen values of a matrix are distinct then the matrix is diagonalizable.

Q: (12) Use the adjoint of matrix to find the third row fourth column element of the inverse of -1 1 4)…

A: Consider the given matrix as A=0-11432-21040110-11. The inverse of the matrix A is given by…

Q: 5. (16 points) Let A = [13¹], B = [-1¹ 63], and C = [29]. Compute each matrix sum or product if it…

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Q: 7. Derive and verify a Cayley-Hamilton formula for the inverse of an invertible 5 × 5 matrix

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Q: b) Evaluate det[(2A)-1 (3A")], where A is any invertible (2 x 2) matrix.

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Q: Compute for the Inverse of Matrix A A=1 2 3 4 A BI E =

A: Given matrix is A = 1234

Q: Which of the following six sets are subrings of M(R)? Which ones have an identity? 0 0 (a) All…

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Q: Let M = -3 2 -3-2 M³ + c₁M² + c₂M + c3I3 = 0, where I3 is the identity 3 x 3 matrix. C1 || S || C3…

A: Here the matrix is given by M=-11-3-3232-32 Here the equation is given by M3+c1M2+c2M+c3…

Q: -2 -2 P with rational D = PT AP. Let A = -4 -4 -13 entries and a diagonal matrix I - -13 Find an…

A: Introduction: A matrix that is both upper and lower triangular is called a diagonal matrix. i.e.,…

Q: го 1 Write the matrix A = 2 1 00 0 1 as a product of elementary matrices.

A: We will write the given matrix as a product of elementary matrices.

Q: [3x 6х —2х] -x 5) The matrix A = , then multiplication of A * A = A? is : a) 6x 2x2! 3x2 -x2] b) x²…

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