The greatest value of c in R for which the sy | vedclass

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

Question

(B) For a system of linear equations to have a non-trivial solution,the determinant of the coefficient matrix must be zero $(D = 0)$.The system is:$x

Vedclass · Accepted Answer

$0.5$

Vedclass · Answer

(B) For a system of linear equations to have a non-trivial solution,the determinant of the coefficient matrix must be zero $(D = 0)$.The system is:$x - cy - cz = 0$$cx - y + cz = 0$$cx + cy - z = 0$The determinant $D$ is given by:$D = \begin{vmatrix} 1 & -c & -c \ c & -1 & c \ c & c & -1 \end{vmatrix} = 0$Expanding the determinant along the first row:$1((-1)(-1) - (c)(c)) - (-c)((c)(-1) - (c)(c)) + (-c)((c)(c) - (-1)(c)) = 0$$1(1 - c^2) + c(-c - c^2) - c(c^2 + c) = 0$$1 - c^2 - c^2 - c^3 - c^3 - c^2 = 0$$-2c^3 - 3c^2 + 1 = 0$$2c^3 + 3c^2 - 1 = 0$Factoring the cubic equation:$(c + 1)^2(2c - 1) = 0$The roots are $c = -1$ (with multiplicity $2$) and $c = \frac{1}{2}$.Therefore,the greatest value of $c$ is $\frac{1}{2}$ or $0.5$.

The greatest value of $c \in R$ for which the system of linear equations $x - cy - cz = 0$,$cx - y + cz = 0$,$cx + cy - z = 0$ has a non-trivial solution,is

Similar Questions

If $a_{1}, a_{2}, a_{3}, \ldots, a_{9}$ are in $AP$,then the value of $\left|\begin{array}{lll}a_{1} & a_{2} & a_{3} \\ a_{4} & a_{5} & a_{6} \\ a_{7} & a_{8} & a_{9}\end{array}\right|$ is

The constant term of the polynomial $\left|\begin{array}{ccc}x+3 & x & x+2 \\ x & x+1 & x-1 \\ x+2 & 2x & 3x+1\end{array}\right|$ is

If the system of equations $ax + y + z = 0$,$x + by + z = 0$ and $x + y + cz = 0$,where $a, b, c \neq 1$,has a non-trivial solution,then the value of $\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}$ is

If the inverse of the matrix $\begin{bmatrix} \alpha & 14 & -1 \\ 2 & 3 & 1 \\ 6 & 2 & 3 \end{bmatrix}$ does not exist,then the value of $\alpha$ is:

If $A \neq O$ and $B \neq O$ are $n \times n$ matrices such that $AB = O$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module