Diagonalizing a Matrix In Exercises 7-14, for each matrix A, find (if possible) a nonsingular matrix P such that P´AP is diagonal. Verify that P1AP is a diagonal matrix with the eigenvalues on the main diagonal. 2. -2 37 A =|0 3 -2 -1 2

Q: Problem 4. Use matrix exponential find general solution of this system : X' = 1 0 X + 0 2 et 3e2t

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Q: 1 3 -4 2 0 0 0 0 0 0 0 0 -1 6. 1 -3 7 1 4 -3 0 0

A: Remark:  We know that the maximum number of linearly independent vectors in a matrix is equal to the…

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Q: 1. For each of the following matrices: (a) Find the eigenvalues of A (b) For each eigenvalue A of A,…

A: A=3102 Finding the eigen value  A-λI=0⇒3-λ102-λ=0⇒λ-3λ-2=0⇒λ=2,3 Finding the eigen value for λ=2…

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A: Given:               x+y+z = 320                                x+12y = 20               y-z = 75

Q: Given the matrix find A³. Write A³ as input your answer below: a11 a12 = a21 = 922 = = -[-3 0 A = A³…

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Q: Use row operations to change the matrix to reduced form. [::] 111 13 45 8 26 111 13 458 26

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Q: 1 For A = i 0 i 0 (1+i)

A: Using row reduction form we have

Q: 3. 1 -4 0. 5-1 2 -5 0 19-13 3-2 3 -2 3.

A: Given matrix are 1−4305−12−503−28 and 1−430019−13−503−28. First transform the first matrix into the…

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A: It is given that, 3-12691-440207413R1.

Q: Find the inverse of the matrix (if it exists).

A: Determinant of the matrix: Since the determinant is not 0, inverse exists

Q: 35-1 -20 4 -20 4 35-1 -42-4 -4 2 -4

A: The solution is given as

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Q: Write down the quadratic form that corresponds to the following 4 -1 -3 -3 1 324

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Q: In Exercises 19-20, compute the following using the given matrix A. a. A³ b. A-3 c. A²2A +I [2 4 19.…

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