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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Byju's Answer

Standard XIII

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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Similar questions

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

Q. Let

A = [\begin{matrix} 0 & a 0 & 0 \end{matrix}]

and

{(A + I)}^{50} - 50 A = [\begin{matrix} a & b c & d \end{matrix}]

, then the value of

a + b + c + d

Q. The value of

∣ ∣ ∣ ∣ ∣ \begin{matrix} 2 & a + b + c + d & a b + c d a + b + c + d & 2 (a + b) (c + d) & a b (c + d) + c d (a + b) a b + c d & a b (c + d) + c d (a + b) & 2 a b c d \end{matrix} ∣ ∣ ∣ ∣ ∣

Q. If

a + b + c + d = 63,

where

a, b, c, d \in I^{+},

then the maximum value of

a b + b c + c d

Let $A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]$ and $B = [\begin{matrix} a & b c & d \end{matrix}]$ are two matrices such that AB = BA and $c \neq 0$ , then value of $\frac{a - d}{3 b - c}$ is :

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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

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