Consider the matrix 4 1 -3 2 1 A = 1 0 1 3 -1 3 -2 -1 3 (a) Find an invertible matrix P that diagonalizes A, and find P-'AP. (b) Without doing any further calculation, use the results of (a) to determine whether A is invertible. Explain your answer.

Q: 26. Let A and B be (2x2) matrices. Prove or find a coun- terexample for this statement: (A - B)(A +…

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A: As per the question we have to find the affine transform which will transform the points A,B,C,D…

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Q: Let I be the identity matrix of nxn. Please Compute the matrix fuunctions COST I

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Q: Create a world transform matrix that translates by 3, 5, 7 and rotates 80° about the x-axis.

A: Detailed explanation mentioned below

Q: a) For invertible matrices A, BE R™×", show that ((AB)")-1 = (A-1)" (B1)". b) Let A, B, C, D e R"*"…

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Q: ^T) + (B^T) and (AB)^T = (A^T)(B^T) if the orders of matrices are appropriate. * False

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Q: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

Q: rmine which of the following matrices is orthogonal. V3 1 (a) (b) V3 0. V3 1- [1 -1 (c) 1 -1 (d) (e)…

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Q: 3.2 Exercises PS2.9 Consider the matrices: A = (a) -2A (b) B-2A 0 -5 -1 -5 B-4 0-1 C= = Compute each…

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Q: Describe all matrices which satisfy det(-A) = -det(A).

A: Assume a square matrix A of order n

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Q: ( -10! BIf (21-A)-! evaluate the matrix A.

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Q: 3. Assume that A is an n × n matrix and A-¹ exists. Prove that (a) (A¹)−¹ – (A−¹)t. (b) (A²)−¹ –…

A: If A is an invertible matrix then AA-1=I (AB)T=BTAT At means interchange rows and columns in a…

Q: How do you know whether a matrix is invertible?

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Q: Diagonalize the matrix 1 0 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix D…

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Q: * Find the Matrix B from order 2 x 4 , Its elements are written in the form by = i + ()

A: Here we find matrix B of order 2×4

Q: 4. Explain what is wrong with the following "proof" that (ABC)" – C"B" A" for three conformable…

A: Properties of transpose of a matrix: (AB)⊥ = B⊥A⊥ Given: (ABC)⊥.

Q: -9 – A 2 Find the greatest value of A that make the matrix A singular. – 6 -2 - A =

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Q: True or False The identity matrix has properties similar tothose of the real number 1.

A: We have to say that the given statement is true or false: The identity matrix has properties similar…

Q: Construct a 3x5 matrix A such that dim Nul 4. Explain and justify your answeT.

A: We need to construct a 3x5 matrix A such that dim Nul A = 4. So, nullity(A) = dim Nul A = 4. We know…

Q: Suppose that n is a positive integer with the properties: • for any integers a, b, c, • n is not…

A: Suppose that n is a positive integer with the properties:1). for any integers a, b, c    2). n is…

Q: Show that matrix multiplication is associative i.e. A(BC) = (AB)C when- ever the multiplication is…

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Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: True or False? Suppose A is an 7 x n matrix. If there is an 7 x n matrix D such that AD = I, then…

A: True. This is a property of invertible matrices, which are square matrices that have an inverse. If…

Q: [2 3 2] 10.) Is A=|0 7 6 an invertible matrix? Explain [5 5 4]

A: We have to solve the problem