Let $A = \begin{bmatrix} 0 & \alpha \ 0 & 0 \end{bmatrix}$ and$(A + 1)^{50} - 50A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$. Then the value Of $a + b + c + d$ is

Question

Dr. Abubacker · Accepted Answer

(a)
We have, $A^{2} = 0,\ A^{k} = 0,\ \forall k \geq 2$
Thus,
$(A + I)^{50} = I + 50A$
$\Rightarrow (A + I)^{50} = I + 50A$
$\Rightarrow a = 1,\ b = 0,\ c = 0,\ d = 1$

Q. Let $A = \begin{bmatrix} 0 & \alpha \\ 0 & 0 \end{bmatrix}$ and$(A + 1)^{50} - 50A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$. Then the value Of $a + b + c + d$ is

Explanation

Reviewed by Dr. Abubacker

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