If A= [ ccc 2 & & -3 0 & 2 & 5 1 & 1 & 3 ], then A^ -1 exists onl… - Vidyadip

MCQ

If $A=\left[\begin{array}{ccc}2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3\end{array}\right]$, then $A^{-1}$ exists only if

A
$\lambda=2$
B
$\lambda \neq 2$
C
$\lambda \neq-2$
✓
$\lambda \neq-8 / 5$

✓

Answer

Correct option: D.

$\lambda \neq-8 / 5$

(d) : $A^{-1}$ exists if $|A| \neq 0$
$
\begin{array}{l}
\text { i.e., }\left|\begin{array}{ccc}
2 & \lambda & -3 \\
0 & 2 & 5 \\
1 & 1 & 3
\end{array}\right| \neq 0 \Rightarrow 2(6-5)+1(5 \lambda+6) \neq 0 \\
\Rightarrow 2+5 \lambda+6 \neq 0 \Rightarrow 5 \lambda \neq-8 \text { i.e., } \lambda \neq \frac{-8}{5}
\end{array}
$

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 Determinants→Determinants — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of $\tan \left[ {{{\sin }^{ - 1}}\left( {\frac{3}{5}} \right) + {{\cos }^{ - 1}}\left( {\frac{3}{{\sqrt {13} }}} \right)} \right]$is

The values of $\theta, \lambda$ for which the following equations $\sin \theta x - cos\theta y + (\lambda +1)z = 0$; $\cos\theta x + \sin\theta\, y - \lambda z = 0$;$ \lambda x +(\lambda + 1)y + \cos\theta z = 0$ have non trivial solution, is

${\tan ^{ - 1}}\left[ {\frac{{\cos x}}{{1 + \sin x}}} \right] = $

The value of $\int\limits_0^2 {\frac{{dx}}{{{{(1 - x)}^2}}}} $ is

The direction ratios of two lines AB, AC are 1, -1, -1 and 2, -1, 1. The direction ratios of the normal to the plane ABC are:

2, 3, −1
2, 2, 1
3, 2, −1
−1, 2, 3

The general solution of the differential equation $\frac{{dy}}{{dx}} = \frac{{{x^2}}}{{{y^2}}}$ is

The value of the definite integral, $\int\limits_0^{\sqrt {\ln \left( {\frac{\pi }{2}} \right)} } {\cos \left( {{e^{{x^2}}}} \right)} {\mkern 1mu} \cdot {\mkern 1mu} 2x{\mkern 1mu} {e^{{x^2}}}dx$ is

Let $x , y , z > 1$ and $A=\left[\begin{array}{lll}1 & \log _x y & \log _x z \\ \log _y x & 2 & \log _y z \\ \log _z x & \log _z y & 3\end{array}\right]$ .Then $\left|\operatorname{adj}\left(\operatorname{adj} A^2\right)\right|$ is equal to

If $\text{P(A)}=\frac{2}{5},\text{P(B)}=\frac{3}{10}$ and $\text{P}(\text{A}\cap\text{B})=\frac{1}{5},$ then, $\text{P}(\overline{\text{A}}|\overline{\text{B}}) \text{ P}(\overline{\text{B}}|\overline{\text{A}})$ is equal to

$\frac{5}{6}$
$\frac{5}{7}$
$\frac{25}{42}$
$1$

If $\theta = {\sin ^{ - 1}}x + {\cos ^{ - 1}}x - {\tan ^{ - 1}}x,x \ge 0$, then the smallest interval in which $\theta $ lies is given by