Number of real values of lambda for which the | vedclass

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

Question

(D) matrix $A$ has no inverse if and only if its determinant is zero,i.e.,$|A| = 0$. Calculating the determinant of $A$: $|A| = \begin{vmatrix} \lambd

Vedclass · Accepted Answer

infinite

Vedclass · Answer

(D) matrix $A$ has no inverse if and only if its determinant is zero,i.e.,$|A| = 0$. Calculating the determinant of $A$: $|A| = \begin{vmatrix} \lambda - 1 & \lambda & \lambda + 1 \ 2 & -1 & 3 \ \lambda + 3 & \lambda - 2 & \lambda + 7 \end{vmatrix}$ Apply the row operation $R_3 ightarrow R_3 - R_1$: $|A| = \begin{vmatrix} \lambda - 1 & \lambda & \lambda + 1 \ 2 & -1 & 3 \ 4 & -2 & 6 \end{vmatrix}$ Notice that row $3$ is exactly $2$ times row $2$ $(R_3 = 2R_2)$. Since two rows are proportional,the determinant of the matrix is $0$ for all real values of $\lambda$. Therefore,the matrix $A$ is singular for all $\lambda \in \mathbb{R}$. Thus,there are infinitely many values of $\lambda$ for which the matrix has no inverse.

Number of real values of $\lambda$ for which the matrix $A = \begin{bmatrix} \lambda - 1 & \lambda & \lambda + 1 \\ 2 & -1 & 3 \\ \lambda + 3 & \lambda - 2 & \lambda + 7 \end{bmatrix}$ has no inverse.

Similar Questions

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

Let $A = \begin{bmatrix} 5 & 5\alpha & \alpha \\ 0 & \alpha & 5\alpha \\ 0 & 0 & 5 \end{bmatrix}$. If $|A|^2 = 25$,then $|\alpha|$ equals:

If $\alpha, \beta, \gamma$ are the roots of the equation $\left|\begin{array}{ccc}x & 2 & 2 \\ 2 & x & 2 \\ 2 & 2 & x\end{array}\right|=0$ and $\min (\alpha, \beta, \gamma)=\alpha$, then $2 \alpha+3 \beta+4 \gamma=$

The number of real values of $t$ such that the system of homogeneous equations
$\begin{aligned}
t x+(t+1) y+(t-1) z &=0 \\
(t+1) x+t y+(t+2) z &=0 \\
(t-1) x+(t+2) y+t z &=0
\end{aligned}$
has non-trivial solutions is

Find the area of the triangle with vertices at the points $(1,0), (6,0), (4,3)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module