Let A- - 0 - 0 0 - and A-I50-50A- - a b- c d - Then- the value of a-b-c-d is

As A^2=O, A^k=O ∀ k ≥ 2 Thus, (A+I)^50=I+50A ⇒ (A+I)^50 50A=I+50A 50A=I ⇒ a=1, b=0, c=0, d=1 a+b+c+d=2 ...

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Standard XII

Mathematics

Equality of Matrices

Let A= [ 0 α;...

Question

$L e t A = [\begin{matrix} 0 & α 0 & 0 \end{matrix}] a n d (A + I)^{50} - 50 A = [\begin{matrix} a & b c & d \end{matrix}], T h e n, t h e v a l u e o f a + b + c + d i s$

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Solution

The correct option is A
2

$A s A^{2} = O, A^{k} = O \forall k \geq 2 T h u s, (A + I)^{50} = I + 50 A \Rightarrow (A + I)^{50} - 50 A = I + 50 A - 50 A = I \Rightarrow a = 1, b = 0, c = 0, d = 1 a + b + c + d = 2$

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LetA=[0α00] and (A+I)50−50A=[abcd],Then, the value of a+b+c+d is

The correct option is A 2 As A2=O, Ak=O ∀ k ≥ 2Thus, (A+I)50=I+50A⇒(A+I)50−50A=I+50A−50A=I⇒a=1, b=0, c=0, d=1a+b+c+d=2

$L e t A = [\begin{matrix} 0 & α 0 & 0 \end{matrix}] a n d (A + I)^{50} - 50 A = [\begin{matrix} a & b c & d \end{matrix}], T h e n, t h e v a l u e o f a + b + c + d i s$

The correct option is A
2

$A s A^{2} = O, A^{k} = O \forall k \geq 2 T h u s, (A + I)^{50} = I + 50 A \Rightarrow (A + I)^{50} - 50 A = I + 50 A - 50 A = I \Rightarrow a = 1, b = 0, c = 0, d = 1 a + b + c + d = 2$