If left[begin{array}{ccc}1 & -1 & x 1 & x & | 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.,$|A| = 0$.Given $A = \left[\begin{array}{ccc}1 & -1 & x \ 1 & x & 1 \ x &

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) matrix $A$ has no inverse if and only if its determinant is zero,i.e.,$|A| = 0$.Given $A = \left[\begin{array}{ccc}1 & -1 & x \ 1 & x & 1 \ x & -1 & 1\end{array}ight]$.Calculating the determinant along the first row:$|A| = 1(x - (-1)) - (-1)(1 - x) + x(-1 - x^2) = 0$$|A| = 1(x + 1) + 1(1 - x) + x(-1 - x^2) = 0$$|A| = x + 1 + 1 - x - x - x^3 = 0$$-x^3 - x + 2 = 0$$x^3 + x - 2 = 0$By inspection,$x = 1$ is a root because $1^3 + 1 - 2 = 0$.Dividing $x^3 + x - 2$ by $(x - 1)$,we get $(x - 1)(x^2 + x + 2) = 0$.For $x^2 + x + 2 = 0$,the discriminant $D = b^2 - 4ac = 1^2 - 4(1)(2) = 1 - 8 = -7$.Since $D Thus,the only real value is $x = 1$.

If $\left[\begin{array}{ccc}1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1\end{array}\right]$ has no inverse,then the real value of $x$ is

Similar Questions

If $\alpha$ is a real root of the equation $x^3+6x^2+5x-42=0$,then the determinant of the matrix $\left[\begin{array}{ccc}\alpha-1 & \alpha+1 & \alpha+2 \\ \alpha-2 & \alpha+3 & \alpha-3 \\ \alpha+4 & \alpha-4 & \alpha+5\end{array}\right]$ is

If $x, y, z$ are in arithmetic progression with common difference $d$,$x \neq 3d$,and the determinant of the matrix $\begin{bmatrix} 3 & 4\sqrt{2} & x \\ 4 & 5\sqrt{2} & y \\ 5 & k & z \end{bmatrix}$ is zero,then the value of $k^2$ is ..... .

The set of all values of $\lambda$ for which the system of linear equations $x - 2y - 2z = \lambda x$,$x + 2y + z = \lambda y$,and $-x - y = \lambda z$ has non-zero solutions.

If $\left| \begin{array}{ccc} a & b & 0 \\ 0 & a & b \\ b & 0 & a \end{array} \right| = 0$,then

The determinant $\left| \begin{array}{ccc} a & b & a\alpha + b \\ b & c & b\alpha + c \\ a\alpha + b & b\alpha + c & 0 \end{array} \right| = 0$,if $a, b, c$ are in

Vedclass Test Series

Exam Paper Generator

Online Exam Module