If $$A=0$$α$$00$$ and $$A+I50-50A=abcd$$ , the value of a $$+$$ b $$+$$ c $$+$$ d is

$$A=0$$α$$00$$ ⇒$$A+I=1$$α$$01$$⇒$$A+I2=1$$α$$011$$α$$01=12$$α$$01$$ $$A+I50=150$$α$$01$$⇒$$A+I50-50A=1001=abcd$$ $$a+b+c+d=2$$

Operations of matrix

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Question

If $A = [\begin{matrix} 0 & α \\ 0 & 0 \end{matrix}]$ and ${(A + I)}^{50} - 50 A = [\begin{matrix} a & b \\ c & d \end{matrix}]$ ,
the value of a + b + c + d is

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Solution

$A = [\begin{matrix} 0 & α \\ 0 & 0 \end{matrix}] \Rightarrow A + I = [\begin{matrix} 1 & α \\ 0 & 1 \end{matrix}] \Rightarrow {(A + I)}^{2} = [\begin{matrix} 1 & α \\ 0 & 1 \end{matrix}] [\begin{matrix} 1 & α \\ 0 & 1 \end{matrix}] = [\begin{matrix} 1 & 2 α \\ 0 & 1 \end{matrix}] {(A + I)}^{50} = [\begin{matrix} 1 & 50 α \\ 0 & 1 \end{matrix}] \Rightarrow {(A + I)}^{50} - 50 A = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] = [\begin{matrix} a & b \\ c & d \end{matrix}] a + b + c + d = 2$

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Operations of matrix

Remember concepts with our Masterclasses.

If A=0α00 and A+I50-50A=abcd , the value of a + b + c + d is

A=0α00 ⇒A+I=1α01⇒A+I2=1α011α01=12α01 A+I50=150α01⇒A+I50-50A=1001=abcd a+b+c+d=2

Ready to Test Your Skills?

free study material

If $A = [\begin{matrix} 0 & α \\ 0 & 0 \end{matrix}]$ and ${(A + I)}^{50} - 50 A = [\begin{matrix} a & b \\ c & d \end{matrix}]$ ,
the value of a + b + c + d is