Download App

Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $A=\left[\begin{array}{cc}2 & 1 \\ -4 & -2\end{array}\right]$, then the value of $I-A+A^2-A^3+\ldots$ is :
  • ✓
    $\left[\begin{array}{cc}-1 & -1 \\ 4 & 3\end{array}\right]$
  • B
    $\left[\begin{array}{cc}3 & 1 \\ -4 & -1\end{array}\right]$
  • C
    $\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$
  • D
    $\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
✓

Answer

Correct option: A.
$\left[\begin{array}{cc}-1 & -1 \\ 4 & 3\end{array}\right]$
Given $A=\left[\begin{array}{cc}2 & 1 \\ -4 & -2\end{array}\right]$, then
$A^2=\left[\begin{array}{cc} 2 & 1 \\ -4 & -2 \end{array}\right]\left[\begin{array}{cc} 2 & 1 \\ -4 & -2 \end{array}\right]$
$=\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right]=0 $
$\Rightarrow A^n=0 \forall n \geq 2$
$\therefore I-A+A^2-A^3+\ldots=I-A$
$=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]-\left[\begin{array}{cc} 2 & 1 \\ -4 & -2 \end{array}\right]$
$=\left[\begin{array}{cc} -1 & -1 \\ 4 & 3 \end{array}\right]$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Matrices→Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The slope of the tangent to the curve $x = t^2 + 3 t - 8, y = 2t^2 - 2t - 5$ at point $(2, -1)$ is :
→
Let $\text{f(x)}\begin{cases}\text{ax}^2+1,&\text{x}<1\\\text{x}+\frac{1}{2},&\text{x}\leq1\end{cases}.$ Then, f(x) is derivable at x = 1, if:
→
The order and degree of the differential equation $\left(y^{\prime \prime \prime}\right)^2+\left(y^{\prime \prime}\right)^3-\left(y^{\prime}\right)^4+y^5=0$ is :
→
If $A_n$ be the area bounded by the curve $y = (\tan x)^n$ and the lines $x = 0, y = 0$ and $\text{x}=\frac{\pi}{4},$ then for $x > 2$
→
The function $F(x) = \int_0^x {\log \left( {\frac{{1 - x}}{{1 + x}}} \right)} \,dx$ is
→
If $f(x) = {\mathop{\rm sgn}} ({x^3})$, then
→
If the feasible region for a solution of linear inequations is bounded, it is called as:
→
Let $g(x)$ be the inverse of the function $f(x)$ and $f'(x) = {1 \over {1 + {x^3}}}$. Then $g'(x)$ is equal to
→
The region represented by the inequation system x, y ≥ 0, y ≤ 6, x + y ≤ 3 is:
→
Statement $- 1:$ The function $x^2 (e^x + e^{-x})$ is increasing for all $x > 0.$

Statement $-2:$ The functions $x^2e^x$ and $x^2e^{-x}$ are increasing for all $x > 0$ and the sum of two increasing functions in any interval $(a, b)$ is an increasing function in $(a, b).$

→