Let T = (tij) be the 7 × 7 matrix with (i, j)-entry tij given by 1,1 ≤ i ≤6, tij 0 for all other i, j. ti,i+1 Is the collection of matrices = = {T, T², T³, T4, T5, T6} linearly independent? Justify your answer.

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A: Given: The equations  06-1-1A+5-534B=4-60-2T0-211A+-4-8-3-6B=3-47-3T

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Q: 9. A = -2 2

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Q: Find all real numbers a, b for which the matrix A nalizable in R. = ( 1] is diago-

A: We have to find all real numbers  for which the matrix  is diagonalizable in

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Q: Q2) Find x for the following matrix 3 1 x| a) -1 3 4= -30 1 ol 1 |1 2 1| b) 12 x 2=0 13 6 xl

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A: Here the given system is: x1+x2=42x1-x2=14 The system in matrix form can be written as:…

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Q: 13. Find all 2 x 2 matrices A = (" such that A? %3D

A: Image is attached with detailed solution.