Question

If A = `[(1,-1,1),(2,1,-3),(1,1,1)]`, then the sum of the elements of A^-1 is ______.

विकल्प

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Answer 1

If A = `[(1,-1,1),(2,1,-3),(1,1,1)]`, then the sum of the elements of A^-1 is 1.

Explanation:

|A| = `|(1,-1,1),(2,1,-3),(1,1,1)|`

= 1(4) + 1(5) + 1(1) = 10 ≠ 0

∴ A^-1 exists.

∴ adj A = `[(4,-5,1),(2,0,-2),(2,5,3)]^"T" = [(4,2,2),(-5,0,5),(1,-2,3)]`

∴ `"A"^-1 = 1/10 [(4,2,2),(-5,0,5),(1,-2,3)]`

∴ sum of the elements of A^-1

`= 1/10 (4 + 2 + 2 - 5 + 0 + 5 + 1 - 2 + 3) = 1`