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Maths-

General

Easy

Question

If D = diag [d₁, d₂, .....d_n] is a diagonal matrix with d_i ≠ 0, i = 1, 2, 3,......, n, then D^–1 is

$d_{1}^{- 1} d_{2}^{- 1}$ ...... $d_{n}^{- 1}$ I_n
diag [ $d_{n}^{- 1}$ , $d_{n - 1}^{- 1}$ , ....... $d_{1}^{- 1}$ ]
diag [ $d_{1}^{- 1}$ $d_{2}^{- 1}$ ...... $d_{n}^{- 1}$ ]
None of these

The correct answer is: diag [ $straight d subscript 1 superscript negative 1 end superscript$ $d subscript 2 end subscript superscript negative 1 end superscript$ ...... $d subscript n end subscript superscript negative 1 end superscript$ ]

Here |D| = d₁d₂d₃ ........d_n and
adj D = [d₂d₃ ........dn, d₁d₃.........d_n, ........ d₁d₂.......d_n_–1]
$rightwards double arrow$ D^–1 = diag [ $d subscript 1 end subscript superscript negative 1 end superscript$ , $d subscript 2 end subscript superscript negative 1 end superscript$ ....... $d subscript n end subscript superscript negative 1 end superscript$ ]

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