Number of real values of for which the matrix A = [ * 20 c - 1 & … - Vidyadip

MCQ

Number of real values of $\lambda$ for which the matrix $A =$ $\left[ {\begin{array}{*{20}{c}}{\lambda - 1}&\lambda &{\lambda + 1}\\2&{ - 1}&3\\ {\lambda + 3}&{\lambda - 2}&{\lambda + 7}\end{array}} \right]$ has no inverse

A
$0$
B
$1$
C
$2$
✓
infinite

✓

Answer

Correct option: D.

infinite

d
$| A | = 0$ for all $\lambda \in R ==> A$ is singular.

Hence inverse can not be found for any value of $\lambda \in R$ ==> $(D)$

Use $R_2 \rightarrow R_2 - (R_3 - R_1)$

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 STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Suppose $y=y(x)$ be the solution curve to the differential equation $\frac{d y}{d x}-y=2-e^{-x}$ such that $\lim _{x \rightarrow \infty} y(x)$ is finite. If $a$ and $b$ are respectively the $x-$ and $y$-intercepts of the tangent to the curve at $x=0$, then the value of $a-4 b$ is equal to$....$

If $\vec{\text{a}}.\vec{\text{b}}=\vec{\text{a}}.\vec{\text{c}}$ and $\vec{\text{a}}\times\vec{\text{b}}=\vec{\text{a}}\times\vec{\text{c}}.\vec{\text{a}}\neq0,$ then :

If $A$ and $B$ are square matrices of same order and $|B| \ne 0$ then $(B^{-1}AB)^5 =$

Let $\quad f:(-\infty, \infty)-\{0\} \rightarrow R$ be a differentiable function such that $f^{\prime}(1)=\lim _{a \rightarrow \infty} a^2 f\left(\frac{1}{a}\right)$.

Then $\lim _{a \rightarrow \infty} \frac{a(a+1)}{2} \tan ^{-1}\left(\frac{1}{a}\right)+a^2-2 \log _e a$ is equal to

Let matrix $A = \left[ {\begin{array}{*{20}{c}}
1&2&3 \\
0&5&4 \\
0&3&2
\end{array}} \right]$ and $A^3 -8A^2 + \alpha A + \beta I = O$ then ordered pair $(\alpha , \beta)$ is

The values of $\alpha $ which satisfy $\int_{\pi /2}^\alpha {\sin x\,dx} $ $ = \sin 2\alpha $, $(\alpha \in [0,\,\,2\pi ])$ are equal to

$\int_{}^{} {{e^x}{{\tan }^2}({e^x})dx = } $

$A$ and $B$ are two given matrices such that the order of $A$ is $3×4$ , if $A’ B$ and $BA’$ are both defined then

$\int\limits^\pi_0\sqrt{\frac{1-\text{x}}{1+\text{x}}}\text{ dx}=$

Let $p$ and $q$ be the position vectors of $P$ and $Q$ respectively with respect to $O$ and $|p|\, = p,\,\,|q|\,\, = q.$ The points $R$ and $S$ divide $PQ$ internally and externally in the ratio $2 : 3$ respectively. If $\overrightarrow {OR} $ and $\overrightarrow {OS} $ are perpendicular, then