The solutions of the equation left| begin{arr | vedclass

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

Question

(A) Let $\Delta = \left| \begin{array}{ccc} 1 & 1 & x \ p+1 & p+1 & p+x \ 3 & x+1 & x+2 \end{array} ight| = 0$. Applying column operations $C_2

Vedclass · Accepted Answer

$x = 1, 2$

Vedclass · Answer

(A) Let $\Delta = \left| \begin{array}{ccc} 1 & 1 & x \ p+1 & p+1 & p+x \ 3 & x+1 & x+2 \end{array} ight| = 0$. Applying column operations $C_2 	o C_2 - C_1$: $\Delta = \left| \begin{array}{ccc} 1 & 0 & x \ p+1 & 0 & p+x \ 3 & x-2 & x+2 \end{array} ight| = 0$. Expanding along the second column: $-(x-2) \left| \begin{array}{cc} 1 & x \ p+1 & p+x \end{array} ight| = 0$. $-(x-2) [ (p+x) - (p+1)x ] = 0$. $-(x-2) [ p + x - px - x ] = 0$. $-(x-2) [ p(1-x) ] = 0$. $p(x-2)(x-1) = 0$. Thus,the solutions are $x = 1$ and $x = 2$.

The solutions of the equation $\left| \begin{array}{ccc} 1 & 1 & x \\ p+1 & p+1 & p+x \\ 3 & x+1 & x+2 \end{array} \right| = 0$ are:

Similar Questions

For $0 < \theta < \frac{\pi}{2}$,if $A = \begin{bmatrix} 1 & -\cos \theta & -1 \\ \cos \theta & 1 & -\cos \theta \\ 1 & \cos \theta & 1 \end{bmatrix}$,then which of the following is true regarding $\operatorname{det}(A)$?

$\left| {\begin{array}{ccc} b + c & a - b & a \\ c + a & b - c & b \\ a + b & c - a & c \end{array}} \right| = $

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 $\left|\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 4 & 5\end{array}\right|=2016 k$,then $k=$ . . . . . .

$\left|\begin{array}{lll}125 & 5 & 25 \\ 343 & 7 & 49 \\ 729 & 9 & 81\end{array}\right|=$ (in $!$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module