Eigenvalues, Eigenvectors and Applications: Question # 2: Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1, 1. -1 -3 2 1 -1 0 Using this diagonalization, write three matrices product in its simplest form for A¹0. Is it same for any power Akfor this special matrix A. 0 1 A

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A: Explanation of the solution is given below...

Q: Community property of multiplication (a+b)(b+c)

A: We find commuting product of multiplication of -  (a+b) (b+C).

Q: B D E (i), (vi) (iii), (v) (iii), (iv) (iii), (vi) (i), (iv) We know the order of A3 is 3. Determine…

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Q: 6x 4x 7x + 40 Compute 7. O6+ 80 + C O 3x + 4x - 7In]x| + 40 + C O 18x+ 8x - 7 +C 2x O 3x + 4x-7in|x|…

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Q: Expand and simplify. (c) (x+2)3

A: According to the question,we have to expand and simplify x+23. As the above expression is algebraic…

Q: Find the rank(A) and null(A). 1 -3 -1 9 . -6 -1 4 -2 -10 -3 9. -6 -6 -3 3 -9 4 9 a) 1; 4 b) 2; 3 c)…

A: Rank(A) and Nullity (A)

Q: x1 X2 x 3 X4 +s +t 4x1 -X1 3x1 - 3x1 -5x2 +4x3 +3x4= 2 +x2 +3x3 +3x4 2 -4x2 +7x3 +6x4 = 4 +3x2 +9x3…

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Q: Example 6

A: The scores of the second attempt is given as- Second attempt 34 31 37 32 40 32 44 37 47 41…

Q: Solve the following recurrence relation with the given initial condition: an = (n + 1)a,n-1 for n =…

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Q: 3x2 + 5 dx. x2 – 3x +2 Evaluate

A: Integrate∫3x2+5x2−3x+2dx

Q: a+1/b = a-1/b + b+1/a

A: Given: a+1/b = a-1/b + b+1/a

Q: A D E (i), (vi) (iii), (v) (iii), (iv) (iii), (vi) (i), (iv) (ii) We know the order of A3 is 3.…

A: