Consider the matrix A 2 (i) Find the characteristic equation of A. (ii) Diagonalise A by computing D, V and V-1 such that A = VDV-¹, where D is a diagonal matrix. (iii) Find A" for all positive integers n.

Q: -2 6. What is the diagonal matrix Find an orthogonal matrix Q that diagonalizes A = 6. A?

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Q: Find the matrix A if 3 1 4 A = 11 00

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Q: matrix P and a matrix C of the form -21 a -b b ces P and Care mma to separate answers as needed.) no…

A: Let    Given that Eigenvalues of A are 5+2I and 5-2i With corresponding eigenvectors are 2+2i-i And…

Q: Solve the matrix equation AX + C = AXB there 1 2 a) A = (-1 ½) · B - (-6 3 ) a = and C = 27 5-1 -22…

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Q: Q2. For the matrix, A = (a) Find 2 Tr (2 A). (b) If A = 21 8 7 4 6 7 5 4 find (A)-².

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Q: A) Justify if the matrix A is diagonalizable.B) Find a matrix T and a diagonal matrix J, such that…

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Q: Express the quadratic form (c₁x₁ + C₂X₂ + ... + Сnn)² in the matrix notation TA, where A is…

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Q: Find an orthogonal diagonalization for A = 1 0 1 0 1 -1 (1888) -1 1 i.e. find an orthogonal matrix U…

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Q: Find a 2 by 2  matrix that scales the point (x,y) by 0.5 in the x direction and 3 in the y…

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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: Find the characteristics equation of the matrix [1 2 A -2 -1 01 and hence find A-.

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Q: Use elementary row operations to determine A-1 (you should be able to do (a) elementary row…

A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

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: (b) Let A be an m × n matrix. Prove that row(A)- = null(A). =

A: Given information: Matrix A is of order m×n. To prove: rowA⊥=nullA Orthogonal complement: Consider V…

Q: 3 Construct a 3 x 3 nonzero matrix A such that the vector 2 is a solution of Ax = 0. A = [(1,2,3),…

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Q: Suppose that 0.3210 approximates 0.3245. How many significant digits does the approximate have? O 3…

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Q: 3. Find m and n so that the matrix below is symmetric:

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Q: Statement: "Let A and B be n x n matrices, where the columns of A span IR" and B is not equal to the…

A: The given statement is false.

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, B be nx n symmetric matrices such that XTAX = X™BX for all %3D column vectors X e R". Show…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Let A, B, C and D be invertible n xn matrices with n> 7, which satisfy the equation ABCT DBA"C = ABT…

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Q: A = [2 -1 0 1; 3 5 7 -1; 1 4 2 7] List the row and column vectors of the matrix.

A: Given :                 A = 2-101; 357-1 ; 1427 To find :               List the row and column…

Q: Use the definition of Ax to write the vector equation as a matrix equation -2 + Z2 - 5 3 +Z4 2 4 Z1…

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Q: Diagonalize the matrix 4. -3 A = 3 -1 1 -2 3 2 by finding a nonsingular matrix S and a diagonal…

A: Given: A=4-3-33-2-3-112To find the characteristic polynomial :…

Q: Use the matrix P to determine if the matrices A and A' are similar. -1 -1 P=[11] 2 p-1 = 6 [2] 15…

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Q: entries

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Q: 1. Let ƒ : R³ → R5 be the function given by f(x₁, x2, X3) = (x₁ + x2 − X3, 2x1 + 2x2 − X3, 3X1 + 3x2…

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