Download App

Determinants — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDeterminants1 Mark
Question
For the matrix $A=\left[\begin{array}{ccc}2 & -1 & 1 \\ \lambda & 2 & 0 \\ 1 & -2 & 3\end{array}\right]$ to be invertible, the value of $\lambda$ is
✓

Answer

Given, $A=\left[\begin{array}{ccc}2 & -1 & 1 \\ \lambda & 2 & 0 \\ 1 & -2 & 3\end{array}\right]$
For invertible matrix, $|A| \neq 0$
So, $2(6-0)+1(3 \lambda-0)+1(-2 \lambda-2) \neq 0$
$\Rightarrow \quad 12+3 \lambda-2 \lambda-2 \neq 0$
$\Rightarrow \lambda+10 \neq 0 \Rightarrow \lambda \neq-10$
$\therefore \quad$ Required value of $\lambda$ is $R-\{-10\}$.

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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Which of these is equal to $\int x e^{x^2} d x$, where $C$ is the constant of integration?
→
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
  1. $\frac{5}{6}$
  2. $\frac{5}{7}$
  3. $\frac{25}{42}$
  4. $1$
→
If $\text{A}= \begin{bmatrix} 1 &\text{amp; } 2 &\text{amp;} 3\end{bmatrix},$ then order is:
  1. 3 × 1
  2. 1 × 3
  3. 2 × 3
  4. None of these
→
The determinant $\begin{vmatrix}\text{b}^2-\text{ab}&\text{b}-\text{c}&\text{bc}-\text{ac}\\\text{ab}-\text{a}^2&\text{a}-\text{b}&\text{b}^2-\text{ab}\\\text{bc}-\text{ac}&\text{c}-\text{a}&\text{ab}-\text{a}^2\end{vmatrix}$ equals:
→
The vector $\cos\alpha\cos\beta\hat{\text{i}}+\cos\alpha\sin\beta\hat{\text{j}}+\sin\alpha\hat{\text{k}}$ is a,
  1. Null vector.
  2. Unit vector.
  3. Constant vector.
  4. None of these.
→
The area of the region bounded by the parabola $y = x^2 + 1$ and the staight line $x + y = 3$ is given by:
→
if x lies in the interval $[0, 1],$ then the least value of $x^2 + x + 1$ is :
→
Choose the correct answer from the given four options.Which of the following is the principal value branch of $\ce{cosec}^{-1}x?$
→
Choose the correct answer from the given four options.
Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5).
Let F = 4x + 6y be the objective function.
The Minimum value of F occurs at.
  1. (0, 2) only.
  2. (3, 0) only.
  3. The mid point of the line sgment joining the points (0, 2) and (3, 0) only.
  4. Any point on the line segment joining the points (0, 2) and (3, 0).
→
The corner points of the bounded feasible region determined by a system of linear constraints are $(0,3),(1,1)$ and $(3,0)$. Let $Z=p x+q y$, where $p, q>0$,. The condition on $p$ and $q$ so that the minimum of $Z$ occurs at $(3,0)$ and $(1,1)$ is
→