If A = [ * 20 c &1 - 1 & - ], then for what value of , , A^2 = O - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}\lambda &1\\{ - 1}&{ - \lambda }\end{array}} \right]$, then for what value of $\lambda ,\,{A^2} = O$

A
$0$
✓
$ \pm {\rm{ }}1$
C
$-1$
D
$1$

✓

Answer

Correct option: B.

$ \pm {\rm{ }}1$

b
(b) ${A^2} = A\,.\,A = \left[ {\begin{array}{*{20}{c}}\lambda &1\\{ - 1}&{ - \lambda }\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}\lambda &1\\{ - 1}&{ - \lambda }\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{{\lambda ^2} - 1}&0\\0&{ - 1 + {\lambda ^2}}\end{array}} \right] = 0$

(As given)

==> ${\lambda ^2} - 1 = 0 \Rightarrow \lambda = \pm 1$.

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 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let the system of linear equations $x +2 y + z =2$, $\alpha x +3 y - z =\alpha,-\alpha x + y +2 z =-\alpha$ be inconsistent. Then $\alpha$ is equal to

Which of the following is a homogeneous differnetial equation?

(4x + 6y + 5)dy - (3y + 2x + 4)dx = 0
xy dx - (x³ + y³)dy = 0
(x³ + 2y²)dx + 2xy dy = 0
y²dx + (x² - xy - y²) = 0

If $\overrightarrow {{{\left| c \right|}^2}} = 60$ and $\overrightarrow c \times \left( {\hat i + 2\hat j + 5\hat k} \right) = \overrightarrow 0 $, then a value of $\overrightarrow c .\left( { - 7\hat i + 2\hat j + 3\hat k} \right)$ is

The vector equation r = i − 2j − k + t(6j − k) represents a straight line passing through the points:

(0, 6, −1) and (1, −2, −1)
(0, 6, −1) and (−1, −4, −2)
(1, −2, −1) and (1, 4, −2)
(1, −2, −1) and (0, −6, 1)

Let f : R → R be a function defined by $\text{f(x)}=\frac{\text{e}^{|\text{x}|}-\text{e}^{-\text{x}}}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}}.$ Then,

f is a bijection.
f is an injection only.
f is surjection on only.
f is neither an injection nor a surjection.

Let $\overrightarrow{ x }$ be a vector in the plane containing vectors $\overrightarrow{ a }=2 \hat{ i }-\hat{ j }+\hat{ k }$ and $\overrightarrow{ b }=\hat{ i }+2 \hat{ j }-\hat{ k }$. If the vector $\overrightarrow{ x }$ is perpendicular to $(3 \hat{ i }+2 \hat{ j }-\hat{ k })$ and its projection on $\overrightarrow{ a }$ is $\frac{17 \sqrt{6}}{2},$ then the value of $|\overrightarrow{ x }|^{2}$ is equal to ...... .

If $\mathrm{P}(\mathrm{A} | \mathrm{B})>\mathrm{P}(\mathrm{A}),$ then which of the following is correct :

The function $f(x) =$ $\sqrt {1 - \sqrt {1 - {x^2}} } $

Let $f : R \rightarrow R$ be a differentiable function such that $f (2) = 2$. Then the value of $\mathop {Limit}\limits_{x\,\, \to \,\,2}\, \int\limits_2^{f\,(x)} {\,\,\frac{{4\,{t^3}}}{{x\, - \,2}}}\,dt$ is

The objective function Z = 4x + 3y can be maximised subjected to the constraints $ 3\text{x}+4\text{y}\leq24,$ $8\text{x}+6\text{y}\leq48,$ $\text{x}\leq5,\text{y}\leq6;\text{x},\text{y}\leq0.$

At only one point
At two points only.
At an infinite number of points.
None of these