Class 12Mathematics3 and 4 .Determinants and MatricesExpansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line
MediumIf $\omega$ is a complex cube root of unity,then $\left| \begin{array}{ccc} 1 & \omega & -\omega^2/2 \\ 1 & 1 & 1 \\ 1 & -1 & 0 \end{array} \right| = $
- A$0$
- B$1$
- C$\omega$
- D$\omega^2$
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The value of the determinant $\left|\begin{array}{lll}b^2-a b & b-c & b c-a c \\ a b-a^2 & a-b & b^2-a b \\ b c-a c & c-a & a b-a^2\end{array}\right|$ is
The area of a triangle is $5$. If two of its vertices are $(2, 1)$ and $(3, -2)$ and the third vertex lies on the line $y = x + 3$,then the third vertex is
MediumIIT 1978
View SolutionThe roots of the equation $\left| \begin{matrix} 0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x \end{matrix} \right| = 0$ are
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View SolutionIf $k = p + q + r$,then the value of $\left|\begin{array}{ccc} k+r & p & q \\ r & k+p & q \\ r & p & k+q \end{array}\right|$ is equal to:
The system of equations $\lambda x + y + z = 0, -x + \lambda y + z = 0, -x - y + \lambda z = 0$ will have a non-zero solution if real values of $\lambda$ are given by
MediumIIT 1984
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