(B) Given the matrix $A = \begin{bmatrix} \lambda & i \\ i & -\lambda \end{bmatrix}$.For the inverse $A^{-1}$ to not exist,the determinant of the matr

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) Given the matrix $A = \begin{bmatrix} \lambda & i \\ i & -\lambda \end{bmatrix}$.For the inverse $A^{-1}$ to not exist,the determinant of the matrix must be zero,i.e.,$|A| = 0$.Calculating the determinant:$|A| = (\lambda)(-\lambda) - (i)(i) = -\lambda^2 - i^2$.Since $i = \sqrt{-1}$,we have $i^2 = -1$.Substituting this into the determinant equation:$|A| = -\lambda^2 - (-1) = -\lambda^2 + 1$.Setting the determinant to zero:$-\lambda^2 + 1 = 0 \Rightarrow \lambda^2 = 1$.Therefore,$\lambda = \pm 1$.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

Easy

If $A = \begin{bmatrix} \lambda & i \\ i & -\lambda \end{bmatrix}$ and $A^{-1}$ does not exist,then $\lambda = $ (where $i = \sqrt{-1}$)

MHT CET 2021 All MHT CET

A
$\pm 2$
B
$\pm 1$
C
$0$
D
$\pm 3$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

3 and 4 .Determinants and Matrices

Subtopic

Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

Previous Year

MHT CET 2021 Paper All MHT CET years →

If the area of a triangle is $4$ sq. units whose vertices are $(k, 0), (4, 0)$ and $(0, 2)$,then the value of $k$ is . . . . . . .

EasyGSEB 2021

View Solution

If the points with position vectors $60 \hat{i}+3 \hat{j}$,$40 \hat{i}-8 \hat{j}$,and $a \hat{i}-52 \hat{j}$ are collinear,then $a$ is equal to

DifficultTS EAMCET 2008

View Solution

The value of $\left|\begin{array}{lll}x & p & q \\ p & x & q \\ p & q & x\end{array}\right|$ is

MediumKCET 2007

View Solution

$A$ set of values of $\theta$ for which the system of equations $(\sin 3 \theta) x-y+z=0$,$(\cos 2 \theta) x+4 y+3 z=0, 2 x+7 y+7 z=0$ has non-trivial solutions,is

EasyAP EAMCET 2018

View Solution

If $x^{3}-2x^{2}-9x+18=0$ and $A=\left|\begin{array}{lll}1 & 2 & 3 \\ 4 & x & 6 \\ 7 & 8 & 9\end{array}\right|$,then the maximum value of $A$ is

DifficultKCET 2021

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $A = \begin{bmatrix} \lambda & i \\ i & -\lambda \end{bmatrix}$ and $A^{-1}$ does not exist,then $\lambda = $ (where $i = \sqrt{-1}$)

Similar Questions

If the area of a triangle is $4$ sq. units whose vertices are $(k, 0), (4, 0)$ and $(0, 2)$,then the value of $k$ is . . . . . . .

If the points with position vectors $60 \hat{i}+3 \hat{j}$,$40 \hat{i}-8 \hat{j}$,and $a \hat{i}-52 \hat{j}$ are collinear,then $a$ is equal to

The value of $\left|\begin{array}{lll}x & p & q \\ p & x & q \\ p & q & x\end{array}\right|$ is

$A$ set of values of $\theta$ for which the system of equations $(\sin 3 \theta) x-y+z=0$,$(\cos 2 \theta) x+4 y+3 z=0, 2 x+7 y+7 z=0$ has non-trivial solutions,is

If $x^{3}-2x^{2}-9x+18=0$ and $A=\left|\begin{array}{lll}1 & 2 & 3 \\ 4 & x & 6 \\ 7 & 8 & 9\end{array}\right|$,then the maximum value of $A$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module