Maharashtra Board Solutions for Chapter: Determinants and Matrices, Exercise 4: MISCELLANEOUS EXERCISE - 4 (A)

The determinant $\mathrm{D}=\left|\begin{array}{ccc}\mathrm{a}& \mathrm{b}& \mathrm{a}+\mathrm{b}\\ \mathrm{b}& \mathrm{c}& \mathrm{b}+\mathrm{c}\\ \mathrm{a}+\mathrm{b}& \mathrm{b}+\mathrm{c}& 0\end{array}\right|$$=0$ If

The value of $a$ for which system of equation $a^3\mathrm{x}+(a+1{)}^3\mathrm{y}+(a+2{)}^3\mathrm{z}=0$, $ax+\left(a+1\right)y+\left(a+2\right)z=0$ and $x+y+z=0$ has non-zero solutions is

$\left|\begin{array}{ccc}\mathrm{b}+\mathrm{c}& \mathrm{c}+\mathrm{a}& \mathrm{a}+\mathrm{b}\\ \mathrm{q}+\mathrm{r}& \mathrm{r}+\mathrm{p}& \mathrm{p}+\mathrm{q}\\ \mathrm{y}+\mathrm{z}& \mathrm{z}+\mathrm{x}& \mathrm{x}+\mathrm{y}\end{array}\right|=$

If $\left|\begin{array}{ccc}6\mathrm{i}& -3\mathrm{i}& 1\\ 4& 3\mathrm{i}& -1\\ 20& 3& \mathrm{i}\end{array}\right|=\mathrm{x}+\mathrm{iy}$ then

If $A(0,0), B(1,3)$ and $C\left(k,0\right)$ are vertices of triangle $ABC$ whose area is $3$ sq.units, then find the value of $k$.

Which of the following is correct

Find the value of $k$ if the following equation are consistent: $(k-2)x+(k-1)y=17,$$(k-1)x+(k-2)y=18$ and $x+y=5$.

Find the value of $k$, if area of triangle is $4$ sq.unit and vertices are $P(k,0), Q(4,0), R(0,2)$.