Let A = a i j be a real matrix of order 3 × 3 , such that a i 1 + a i 2 + a i 3 = 1 , for i = 1 , 2 , 3 . Then, the sum of all the entries of the matrix A 3 is equal to:

Question

Let A = a i j be a real matrix of order 3 &#215; 3 , such that a i 1 + a i 2 + a i 3 = 1 , for i = 1 , 2 , 3 . Then, the sum of all the entries of the matrix A 3 is equal to:

Quantrex Academy · Accepted Answer

Correct answer: C. 3

Given A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 Let, X = 1 1 1 Then, we have A X = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 1 1 1 &#8658; a 11 + a 12 + a 13 a 21 + a 22 + a 23 a 31 + a 32 + a 33 Given, a i 1 + a i 2 + a i 3 = 1 , for i = 1 , &#160; 2 , &#160; 3 &#8658; a 11 + a 12 + a 13 a 21 + a 22 + a 23 a 31 + a 32 + a 33 = 1 1 1 &#8658; A X = X &#160; &#160; &#160; . . . i Pre multiply by A , we get A 2 X = A X &#160; &#160; &#160; . . . i i From i &#160; &#38; &#160; i i , we get A 2 X = X Again, pr

Let A = a i j be a real matrix of order 3 × 3 , such that a i 1 + a i 2 + a i 3 = 1 , for i = 1 , 2 , 3 . Then, the sum of all the entries of the matrix A 3 is equal to:

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Correct answer

Step-by-step solution

More from Matrices

Let A = a i j be a real matrix of order 3 &#215; 3 , such that a i 1 + a i 2 + a i 3 = 1 , for i = 1 , 2 , 3 . Then, the sum of all the entries of the matrix A 3 is equal to:

Options

Correct answer

Step-by-step solution

More from Matrices

Let A = a i j be a real matrix of order 3 × 3 , such that a i 1 + a i 2 + a i 3 = 1 , for i = 1 , 2 , 3 . Then, the sum of all the entries of the matrix A 3 is equal to: