The values of x for which the given matrix le | vedclass

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

Question

(B) Let $A = \left[\begin{array}{ccc}-x & x & 2 \ 2 & x & -x \ x & -2 & -2\end{array}ight]$.$A$ matrix $A$ is non-singular if and only if its dete

Vedclass · Accepted Answer

for all $x$ other than $2$ and $-2$

Vedclass · Answer

(B) Let $A = \left[\begin{array}{ccc}-x & x & 2 \ 2 & x & -x \ x & -2 & -2\end{array}ight]$.$A$ matrix $A$ is non-singular if and only if its determinant $|A| 
eq 0$.Calculating the determinant $|A|$:$|A| = -x \begin{vmatrix} x & -x \ -2 & -2 \end{vmatrix} - x \begin{vmatrix} 2 & -x \ x & -2 \end{vmatrix} + 2 \begin{vmatrix} 2 & x \ x & -2 \end{vmatrix}$$|A| = -x(-2x - 2x) - x(-4 + x^2) + 2(-4 - x^2)$$|A| = -x(-4x) + 4x - x^3 - 8 - 2x^2$$|A| = 4x^2 + 4x - x^3 - 8 - 2x^2$$|A| = -x^3 + 2x^2 + 4x - 8$For the matrix to be non-singular,$|A| 
eq 0$:$-x^3 + 2x^2 + 4x - 8 
eq 0$$-(x^3 - 2x^2 - 4x + 8) 
eq 0$$-(x^2(x - 2) - 4(x - 2)) 
eq 0$$-(x^2 - 4)(x - 2) 
eq 0$$-(x - 2)(x + 2)(x - 2) 
eq 0$$-(x - 2)^2(x + 2) 
eq 0$Therefore,$x 
eq 2$ and $x 
eq -2$.Thus,the matrix is non-singular for all $x$ other than $2$ and $-2$.

The values of $x$ for which the given matrix $\left[\begin{array}{ccc}-x & x & 2 \\ 2 & x & -x \\ x & -2 & -2\end{array}\right]$ will be non-singular are

Similar Questions

Which of the following is correct?

If $q_1, q_2, q_3$ are roots of the equation $x^3 + 64 = 0$,then the value of $\left| \begin{array}{ccc} q_1 & q_2 & q_3 \\ q_2 & q_3 & q_1 \\ q_3 & q_1 & q_2 \end{array} \right|$ is

Evaluate the determinant: $\left|\begin{array}{cc}\sin \frac{11 \pi}{36} & \cos \frac{11 \pi}{36} \\\sin \frac{2 \pi}{9} & \cos \frac{2 \pi}{9}\end{array}\right|$.

If $a, b, c$ are real,then the value of the determinant $\left| {\begin{array}{*{20}{c}} {{a^2} + 1}&{ab}&{ac}\\{ab}&{{b^2} + 1}&{bc}\\{ac}&{bc}&{{c^2} + 1}\end{array}}\right| = 1$ if

If $a, b, c$ are in $A.P.$,then the determinant $\left|\begin{array}{lll}x+2 & x+3 & x+2a \\ x+3 & x+4 & x+2b \\ x+4 & x+5 & x+2c\end{array}\right|$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module