First slide

Operations of matrix

Question

If $D = diag (d_{1}, d_{2}, d_{3}, \dots, d_{n}),$ where $d_{i} \neq 0$ for all i =1,2,.. n, then D^-1 is equal to

Moderate

A

D
B

$diag (d_{1}^{- 1}, d_{2}^{- 1}, \dots, d_{n}^{- 1})$
C

$I_{n}$
D

None of these

Solution

$D = diag (d_{1}, d_{2}, d_{3}, \dots, d_{n}), |D| = d_{1} d_{2} d_{3} . . . \dots d_{n} AdjD = diag (d_{2} d_{3} . . . \dots d_{n}, d_{1} d_{3} . . . \dots d_{n}, . . . . . . . . ., d_{1} d_{2} d_{3} . . . \dots d_{n - 1}) D^{- 1} = \frac{AdjD}{|D|} = diag (d_{1}^{- 1}, d_{2}^{- 1}, \dots, d_{n}^{- 1})$

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