For how many value (s) of x in the closed interval [ - 4, , , - 1… - Vidyadip

MCQ

For how many value $(s)$ of $x$ in the closed interval $[ - 4,\,\, - 1]$ is the matrix $\left[ {\begin{array}{*{20}{c}}3&{ - 1 + x}&2\\3&{ - 1}&{x + 2}\\{x + 3}&{ - 1}&2\end{array}} \right]$ singular

A
$2$
B
$0$
C
$3$
✓
$1$

✓

Answer

Correct option: D.

$1$

d
(d) For the given matrix to be singular, we must have, $\left| {\,\begin{array}{*{20}{c}}3&{ - 1 + x}&2\\3&{ - 1}&{x + 2}\\{x + 3}&{ - 1}&2\end{array}\,} \right|\, = 0$
==> $\left| {\,\begin{array}{*{20}{c}}3&{ - 1 + x}&2\\0&{ - x}&x\\x&{ - x}&0\end{array}\,} \right|\, = 0$, $\,[{R_2} \to {R_2} - {R_1},\,{R_3} \to {R_3} - {R_1}]$
==> $\left| {\,\begin{array}{*{20}{c}}{x + 4}&{ - 1 + x}&2\\0&{ - x}&x\\0&{ - x}&0\end{array}\,} \right|\, = 0$, $[{C_1} \to {C_1} + {C_2} + {C_3}]$
==> $(x + 4)\,(0 + {x^2}) = 0 \Rightarrow x = - 4,\,0$
Note that only $ - 4 \in [ - 4,\, - 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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A chord $AB$ drawn from the point $A(0,3)$ on circle ${x^2} + 4x + {(y - 3)^2} = 0$ meets to $M$ in such a way that $AM = 2AB$, then the locus of point $M$ will be

Number of points where the function $f(x) = $ maximum $\left( {\sqrt {2x - {x^2}} ,2 - x} \right)$ is non differentiable is

$\cos 20^\circ \cos 40^\circ \cos 80^\circ = $

Area of the triangle formed by the lines $x -y = 0, x + y = 0$ and any tangent to the hyperbola $x^2 -y^2 = a^2$ is :-

The ${n^{th}}$ term of series $\frac{1}{1} + \frac{{1 + 2}}{2} + \frac{{1 + 2 + 3}}{3} + .......$ will be

If ${z_1},{z_2} \in C$, then $amp\,\left( {\frac{{{{\rm{z}}_{\rm{1}}}}}{{{{{\rm{\bar z}}}_{\rm{2}}}}}} \right) = $

Considering the principal values of the inverse trigonometric functions, $\sin ^{-1}\left(\frac{\sqrt{3}}{2} x+\frac{1}{2} \sqrt{1-x^{2}}\right),-\frac{1}{2} < x < \frac{1}{\sqrt{2}}$, is equal to

The coordiantes of the ends of a focal chord of a parabola $y^2 = 4ax $ are $(x_1, y_1) $ and $(x_2, y_2) $ then $x_1x_2 + y_1y_2 $ has the value equal to

Let the first term of a series be $T_1=6$ and its $\mathrm{r}^{\text {th }}$ term $T_r=3 T_{r-1}+6^r, r=2,3, \ldots . ., n$. If the sum of the first $\mathrm{n}$ terms of this series is $\frac{1}{5}\left(n^2-12 n+39\right)$ $\left(4.6^n-5.3^n+1\right)$. Then $n$ is equal to ...........

In how many ways can $5$ keys be put in a ring