Class 12Mathematics3-4. Matrices and DeterminantsExpansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line
Easyयदि $\left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right|$ है,तो $x$ का मान ज्ञात कीजिए:
- A$2$
- B$4$
- C$8$
- D$\pm 2 \sqrt{2}$
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यदि $abc \neq 0$ है और समीकरण निकाय $x+7ay+2az=0$,$x+6by+2bz=0$,$x+5cy+2cz=0$ का एक अशून्य हल है,तो $a, b, c$ किसमें हैं
माना $A=\begin{bmatrix} 2 & 2+p & 2+p+q \\ 4 & 6+2p & 8+3p+2q \\ 6 & 12+3p & 20+6p+3q \end{bmatrix}$ है। यदि $\operatorname{det}(\operatorname{adj}(\operatorname{adj}(3A)))=2^m \cdot 3^n$,जहाँ $m, n \in N$,तो $m+n$ का मान ज्ञात कीजिए:
सारणिक $\left|\begin{array}{lll}b^2-a b & b-c & b c-a c \\ a b-a^2 & a-b & b^2-a b \\ b c-a c & c-a & a b-a^2\end{array}\right|$ का मान है
यदि $\left| {\begin{array}{*{20}{c}}{{x^2} + x}&{x + 1}&{x - 2}\\ {2{x^2} + 3x - 1}&{3x}&{3x - 3}\\ {{x^2} + 2x + 3}&{2x - 1}&{2x - 1}\end{array}} \right| = Ax - 12$ है,तो $A$ का मान ज्ञात कीजिए।
यदि $A = \begin{bmatrix} \alpha^2 & 5 \\ 5 & -\alpha \end{bmatrix}$ और $\det(A^{10}) = 1024$ है,तो $\alpha = $
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