If $A = \left[ {\begin{array}{*{20}{c}} 1&2\\ 3&4 \end{array}} \right],$ then $I + A + {A^2} + {A^3} + \ldots \infty $ equals to

$\left[ {\begin{array}{*{20}{c}} {1/2}&{ - 1/3}\\ { - 1/2}&0 \end{array}} \right]$

$\left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right]$

$\left[ {\begin{array}{*{20}{c}} { - 1}&{ - 2}\\ { - 3}&{ - 4} \end{array}} \right]$

$\left[ {\begin{array}{*{20}{c}} { - 1/4}&{1/3}\\ {1/2}&0 \end{array}} \right]$

Back to MATRICES

JEE MATHEMATICS MCQ: MATRICES

1 Easy

1 of 1

Application +4 | -1

A = \left[ {\begin{array}{cccccccccccccccccccc} 1&2\\ 3&4 \end{array}} \right],

then

I + A + {A^2} + {A^3} + \ldots \infty

equals to

View answer and explanation

Correct option: C

\left[ {\begin{array}{cccccccccccccccccccc} {1/2}&{ - 1/3}\\ { - 1/2}&0 \end{array}} \right]

The correct answer is C. The sum of the infinite matrix series can be found by using the formula for the sum of an infinite geometric series and then inverting the resulting matrix.

More Questions from MATRICES

Practice All Chapter MCQs →

\left|\begin{array}{ccc}a & b-c & b+c \\ c+a & b & c-a \\ a-b & a+b & c\end{array}\right|=0

and

a, b, c

are real numbers then the line

a x+b y+c=0

passes through the fixed point is The number of solutions of the system of equations

{x_2} - {x_3} = 1,\; - {x_1} + 2{x_3} = - 2,\;{x_1} - 2,\;{x_1} - 2{x_2} = 3

is If the equations

2x + 3y + 1 = 0,3x + y - 2 = 0

and

ax + 2y - b = 0

are consistent, then The value of the determinant

\left|\begin{array}{ccc}1 & \left(\alpha^{2 x}-\alpha^{-2 x}\right)^2 & \left(\alpha^{2 x}+\alpha^{-2 x}\right)^2 \\ 1 & \left(\beta^{2 x}-\beta^{-2 x}\right)^2 & \left(\beta^{2 x}+\beta^{-2 x}\right)^2 \\ 1 & \left(\gamma^{2 x}-\gamma^{-2 x}\right)^2 & \left(\gamma^{2 x}+\gamma^{-2 x}\right)^2\end{array}\right|

, is If

\omega

is the cube root of unity, then

\left| {\begin{array}{cccccccccccccccccccc} 1&\omega &{{\omega ^2}}\\ \omega &{{\omega ^2}}&1\\ {{\omega ^2}}&1&\omega \end{array}} \right|

is equal to For any matrix

A

of order

2 \times 2

, if

A(\operatorname{adj} A)=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]

, then

|A|

is equal to