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Maths-

General

Easy

Question

If D = diag (d₁, d₂,.....,d_n), then Dⁿ equals -

D
diag (d₁^n–1, d₂^n–1, ....d_n^n–1)
diag (d₁ⁿ, d₂ⁿ, .....,d_nⁿ)
None of these

The correct answer is: diag (d₁ⁿ, d₂ⁿ, .....,d_nⁿ)

we are given that D = diag (d1, d2,.....,dn) and we need to find what Dn equals -
$A space d i a g o n a l space m a t r i x space i s space a space s q u a r e space m a t r i x space i n space w h i c h space t h e space e n t r i e s space o u t s i d e space t h e space m a i n space d i a g o n a l space a r e space a l l space z e r o s. T h e r e f o r e space t h e space d e t e r m i n a n t s space o f space d i a g o n a l space m a t r i x space g i v e s space t h e space m u l t i p l i c a t i o n space o f space d i a g o n a l space e l e m e n t s D to the power of n space end exponent equals space D. D. D. D. D......... D left parenthesis U p t o space n space t i m e s right parenthesis open square brackets table row cell d 1 end cell 0 cell..... end cell 0 row 0 cell d 2 end cell cell..... end cell cell... end cell row.. cell... end cell cell d n end cell end table close square brackets open square brackets table row cell d 1 end cell 0 cell..... end cell 0 row 0 cell d 2 end cell cell..... end cell cell... end cell row.. cell... end cell cell d n end cell end table close square brackets space............. equals open square brackets table row cell d 1 to the power of n end cell 0 cell..... end cell 0 row 0 cell d 2 to the power of n end cell cell..... end cell cell... end cell row.. cell... end cell cell d n to the power of n end cell end table close square brackets equals d i a g left square bracket space d 1 to the power of n space d 2 to the power of n space d 3 to the power of n space........ space space d n to the power of n space right square bracket$

Therefore the correct option is choice 3

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