Let the matrix A= 1 1 2 2 and B=A+A^2+A^3+A^4. If B=λA, ∀λ∈R, then the value of λ is equal to

Correct answer: 40. A^2= 1 1 2 2 1 1 2 2 = 3 3 6 6 =3A Hence, A^3=3A^2=9A,A^4=27A So, B=1+3+9+27A=40A

Q19 / 75 · NTA Abhyas (JEE Main) 2020 · Mathematics · Matrices

Let the matrix $A = [\begin{matrix} 1 & 1 \\ 2 & 2 \end{matrix}]$ and $B = A + A^{2} + A^{3} + A^{4} .$ If $B = λ A, \forall λ \in R,$ then the value of $λ$ is equal to

Correct answer: 40

A^{2} = [\begin{matrix} 1 & 1 \\ 2 & 2 \end{matrix}] [\begin{matrix} 1 & 1 \\ 2 & 2 \end{matrix}] = [\begin{matrix} 3 & 3 \\ 6 & 6 \end{matrix}] = 3 A

Hence,

A^{3} = 3 A^{2} = 9 A, A^{4} = 27 A

So,

B = (1 + 3 + 9 + 27) A = 40 A

Hence, the correct answer is 40.