(B) square matrix $A$ is invertible if and only if its determinant is non-zero,i.e.,$|A| \neq 0$.Given the matrix $A = \begin{bmatrix} \lambda & -1 &

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

(B) square matrix $A$ is invertible if and only if its determinant is non-zero,i.e.,$|A| \neq 0$.Given the matrix $A = \begin{bmatrix} \lambda & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2 \end{bmatrix}$.Calculating the determinant $|A|$:$|A| = \lambda(0 \times 2 - 1 \times 1) - (-1)(-3 \times 2 - 1 \times (-1)) + 4(-3 \times 1 - 0 \times (-1))$$|A| = \lambda(0 - 1) + 1(-6 + 1) + 4(-3 - 0)$$|A| = -\lambda - 5 - 12$$|A| = -\lambda - 17$For the matrix to be invertible,$|A| \neq 0$:$-\lambda - 17 \neq 0$$-\lambda \neq 17$$\lambda \neq -17$.

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

Easy

The matrix $\begin{bmatrix} \lambda & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2 \end{bmatrix}$ is invertible,if

A
$\lambda \neq -15$
B
$\lambda \neq -17$
C
$\lambda \neq -16$
D
$\lambda \neq -18$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

3-4. Matrices and Determinants

Subtopic

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

The area of a triangle with vertices $(-3, 0)$, $(3, 0)$, and $(0, k)$ is $9$ sq units. Find the possible values of $k$.

DifficultKCET 2023

View Solution

If $\omega$ is a cube root of unity,then $\left| \begin{array}{ccc} x + 1 & \omega & \omega^2 \\ \omega & x + \omega^2 & 1 \\ \omega^2 & 1 & x + \omega \end{array} \right| = $

Easy

View Solution

If the area of a triangle is $35$ sq. units with vertices $(2, -6)$, $(5, 4)$, and $(k, 4)$, then $k$ is . . . . . . .

DifficultGUJCET 2026

View Solution

Evaluate the determinant: $\left|\begin{array}{ccc}1 & a & b \\ 1 & a+b & b \\ 1 & a & a+b\end{array}\right| = $ . . . . . . .

EasyGSEB 2017

View Solution

If the determinant $\left|\begin{array}{ccc}\cos 2x & \sin^2 x & \cos 2x \\ \sin^2 x & \cos 2x & \cos^2 x \\ \cos 2x & \cos^2 x & \cos 2x\end{array}\right|$ is expanded in powers of $\cos x$,then the constant term in the expansion is

MediumAP EAMCET 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

The matrix $\begin{bmatrix} \lambda & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2 \end{bmatrix}$ is invertible,if

Similar Questions

The area of a triangle with vertices $(-3, 0)$, $(3, 0)$, and $(0, k)$ is $9$ sq units. Find the possible values of $k$.

If $\omega$ is a cube root of unity,then $\left| \begin{array}{ccc} x + 1 & \omega & \omega^2 \\ \omega & x + \omega^2 & 1 \\ \omega^2 & 1 & x + \omega \end{array} \right| = $

If the area of a triangle is $35$ sq. units with vertices $(2, -6)$, $(5, 4)$, and $(k, 4)$, then $k$ is . . . . . . .

Evaluate the determinant: $\left|\begin{array}{ccc}1 & a & b \\ 1 & a+b & b \\ 1 & a & a+b\end{array}\right| = $ . . . . . . .

If the determinant $\left|\begin{array}{ccc}\cos 2x & \sin^2 x & \cos 2x \\ \sin^2 x & \cos 2x & \cos^2 x \\ \cos 2x & \cos^2 x & \cos 2x\end{array}\right|$ is expanded in powers of $\cos x$,then the constant term in the expansion is

Vedclass Test Series

Exam Paper Generator

Online Exam Module