Question
Solve the following equations.
i) $\left|\begin{array}{lll}x & 2 & 2 \\ 2 & x & 2 \\ 2 & 2 & x\end{array}\right|=0$
ii) $\left|\begin{array}{ccc}1 & 4 & 20 \\ 1 & -2 & 5 \\ 1 & 2 x & 5 x^2\end{array}\right|=0$

Answer

Get the step-by-step solution for this question inside the Vidyadip app.

Get the answer in the app

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

Without expanding the determinants, show that:
i) $\left|\begin{array}{lll}b+c & b c & b^2 c^2 \\ c+a & c a & c^2 a^2 \\ a+b & a b & a^2 b^2\end{array}\right|=0$
ii)$\left|\begin{array}{ccc}x a & y b & z c \\ a^2 & b^2 & c^2 \\ 1 & 1 & 1\end{array}\right|$ =$\left|\begin{array}{ccc}x & y & z \\ a & b & c \\ b c & c a & a b\end{array}\right|$
iii) $\left|\begin{array}{lll}l & m & n \\ e & d & f \\ u & v & w\end{array}\right|=\left|\begin{array}{lll}n & f & w \\ l & e & u \\ m & d & v\end{array}\right|$
iv) $\left|\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right|=0$
Find the value(s) of $x$, if
i) $\left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|=\left|\begin{array}{cc}x & 3 \\ 2 x & 5\end{array}\right|$
ii) $\left|\begin{array}{ccc}2 & 1 & x+1 \\ -1 & 3 & -4 \\ 0 & -5 & 3\end{array}\right|=0$
iii) $\left|\begin{array}{ccc}x-1 & x & x-2 \\ 0 & x-2 & x-3 \\ 0 & 0 & x-3\end{array}\right|=0$
If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A’ ∩ B’) = 5, find
(i) n(A ∪ B)
(ii) n(A ∩ B)
(iii) n(A’ ∩ B)
(iv) n(A ∩ B’)
Evaluate the following determinants:
1. $\left|\begin{array}{cc}4 & 7 \\ -7 & 0\end{array}\right|$
2. $\left|\begin{array}{ccc}3 & -5 & 2 \\ 1 & 8 & 9 \\ 3 & 7 & 0\end{array}\right|$
3. $\left|\begin{array}{lll}1 & i & 3 \\ i^3 & 2 & 5 \\ 3 & 2 & i^4\end{array}\right|$
4. $\left|\begin{array}{lll}5 & 5 & 5 \\ 5 & 4 & 4 \\ 5 & 4 & 8\end{array}\right|$
5. $\left|\begin{array}{cc}2 i & 3 \\ 4 & -i\end{array}\right|$
6. $\left|\begin{array}{ccc}3 & -4 & 5 \\ 1 & 1 & -2 \\ 2 & 3 & 1\end{array}\right|$
7. $\left|\begin{array}{lll}a & h & g \\ h & b & f \\ g & f & c\end{array}\right|$
8. $\left|\begin{array}{ccc}0 & a & -b \\ -a & 0 & -c \\ b & c & 0\end{array}\right|$
If $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cl}4 x-2, & x \leq-3 \\ 5, & -3<x<3, \text { then fmd } \\ x^2, & x \geq 3\end{array}\right.$
(i) $\mathrm{f}(-4)$
(ii) $f(-3)$
(iii) $f(1)$
(iv) $f(5)$
If $A=\left\{x / 6 x^2+x-15=0\right\}, B=\left\{x / 2 x^2-5 x-3=0\right\}, C=\left\{x / 2 x^2-x-3=0\right\}$, then find (i) $(A \cup B \cup C)($ ii $)(A \cap B \cap C)$
Find the slope, x-intercept, y-intercept of each of the following lines.
(a) 2x + 3y – 6 = 0
(b) x + 2y = 0
If $f(x)=3 x+5, g(x)=6 x-1$, then find
(i) $(f+g)(x)$
(ii) $(f-g)(2)$
(iii) $(\mathrm{fg})(3)$
(iv) $\left(\frac{\mathbf{f}}{\mathbf{g}}\right)(x)$ and its domain

Image

Image
Find the equation of the line:
(i) having slope 5 and containing point $A(-1,2)$.
(ii) containing the point $(2,1)$ and having slope 13 .
(iii) containing the point $\mathrm{T}(7,3)$ and having inclination $90^{\circ}$.
(iv) containing the origin and having inclination $90^{\circ}$.
(v) through the origin which bisects the portion of the line $3 x+2 y=2$ intercepted between the co-ordinate axes.