The matrix [ * 20 c 2& & - 4 - 1 &3&4 1& - 2 & - 3 ]is non singul… - Vidyadip

MCQ

The matrix $\left[ {\begin{array}{*{20}{c}}2&\lambda &{ - 4}\\{ - 1}&3&4\\1&{ - 2}&{ - 3}\end{array}} \right]$is non singular, if

✓
$\lambda \ne - 2$
B
$\lambda \ne 2$
C
$\lambda \ne 3$
D
$\lambda \ne - 3$

✓

Answer

Correct option: A.

$\lambda \ne - 2$

a
(a) The given matrix $A = \left[ {\begin{array}{*{20}{c}}2&\lambda &{ - 4}\\{ - 1}&3&4\\1&{ - 2}&{ - 3}\end{array}} \right]$ is non singular, if $|A|\, \ne 0$

$|A|\,\, = \left| {\,\begin{array}{*{20}{c}}2&\lambda &{ - 4}\\{ - 1}&3&4\\1&{ - 2}&{ - 3}\end{array}\,} \right|\,$=$\left| {\,\begin{array}{*{20}{c}}1&{\lambda + 3}&0\\{ - 1}&3&4\\1&{ - 2}&{ - 3}\end{array}\,} \right|\,$,$[{R_1} \to {R_2} + {R_1}]$

= $\left| {\,\begin{array}{*{20}{c}}1&{\lambda + 3}&0\\0&1&1\\0&{ - \lambda - 5}&{ - 3}\end{array}\,} \right|$$\left[ {\begin{array}{*{20}{c}}{{R_2} \to {R_2} + {R_3}}\\{{R_3} \to {R_3} - {R_1}}\end{array}} \right]$

= $1\,( - 3 + \lambda + 5) \ne 0$

$ \Rightarrow \lambda + 2 \ne 0$ $ \Rightarrow \lambda \,\, \ne - 2.$

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

If points (1, 2), (3, 5) and (0, b) are collinear the value of b is:

$\frac{1}{2}$
$\frac{7}{2}$
$2$
$-1$

If in a $\triangle\text{ABC}$, $\text{A}=(0,0),\ \text{B}=(3,3\sqrt3),\ \text{C}=(-3\sqrt3,3)$, then the vecctor of magnitude $2\sqrt2$ units directed along AO, where O is the circumcenter of $\triangle\text{ABC}$ is,

$(1-\sqrt3)\hat{\text{i}}+(1+\sqrt3)\hat{\text{j}}$
$(1+\sqrt3)\hat{\text{i}}+(1-\sqrt3)\hat{\text{j}}$
$(1+\sqrt3)\hat{\text{i}}+(\sqrt3-1)\hat{\text{j}}$
None of these

Three concurrent edges $ OA, OB, OC$ of a parallelopiped are represented by three vectors $2i + j - k,\,\,i + 2j + 3k$ and $ - 3i - j + k,$ the volume of the solid so formed in cubic unit is

If $\sin^{-1}\Big(\frac{2\text{a}}{1-\text{a}^2}\Big)+\cos^{-1}\Big(\frac{1-\text{a}^2}{1+\text{a}^2}\Big)=\tan^{-1}\Big(\frac{2\text{x}}{1-\text{x}^2}\Big),$ where $\text{a},\text{x}\in(0,1),$ then the value of x is:

$0$
$\frac{\text{a}}{2}$
$\text{a}$
$\frac{2\text{a}}{1-\text{a}^2}$

If $f(x) f(y)=f(x+y)$ for all $x, y$; suppose $f(5)=2$ and $f^{\prime}(0)=3$, then $f^{\prime}(5)$ is equal to

The value of $\int_{\,0}^{\,\pi /2} {\frac{{{2^{\sin x}}}}{{{2^{\sin x}} + {2^{\cos x}}}}dx} $ is

The integrating factor of the differential equation$(1-\text{y}^{2})\frac{\text{dx}}{\text{dy}}+\text{yx}=\text{ay}(-1<\text{y}<1)$ is:

$\frac{1}{\text{y}^{2}-1}$
$\frac{1}{\sqrt{\text{y}^{2}+1}}$
$\frac{1}{1-\text{y}^{2}}$
$\frac{1}{\sqrt{1-\text{y}^{3}}}$

The area of the region formed by $\text{x}^2+\text{y}^2-6\text{x}-4\text{y}+12\leq0,\text{ y}\leq\text{x}$ and $\text{x}\leq\frac{5}{2}$

$\frac{\pi}{6}-\frac{\sqrt{3}+1}{8}$
$\frac{\pi}{6}+\frac{\sqrt{3}+1}{8}$
$\frac{\pi}{6}-\frac{\sqrt{3}-1}{8}$
none of these

A binary operation * on Z defined by a * b = 3a + b for all a, b ∈ Z, is:

Commutative.
Associative.
Not commutative.
Commutative and associative.

The constraints $x+y \leq 4,3 x+3 y \geq 18, x \geq 0, y \geq 0$ defines on