Class 12Mathematics3-4. Matrices and DeterminantsExpansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line
Mediumજો $2x + 3y - 5z = 7$,$x + y + z = 6$,અને $3x - 4y + 2z = 1$ હોય,તો $x =$
- A$\left| \begin{array}{ccc} 2 & -5 & 7 \\ 1 & 1 & 6 \\ 3 & 2 & 1 \end{array} \right| \div \left| \begin{array}{ccc} 7 & 3 & -5 \\ 6 & 1 & 1 \\ 1 & -4 & 2 \end{array} \right|$
- B$\left| \begin{array}{ccc} -7 & 3 & -5 \\ -6 & 1 & 1 \\ -1 & -4 & 2 \end{array} \right| \div \left| \begin{array}{ccc} 2 & 3 & -5 \\ 1 & 1 & 1 \\ 3 & -4 & 2 \end{array} \right|$
- C$\left| \begin{array}{ccc} 7 & 3 & -5 \\ 6 & 1 & 1 \\ 1 & -4 & 2 \end{array} \right| \div \left| \begin{array}{ccc} 2 & 3 & -5 \\ 1 & 1 & 1 \\ 3 & -4 & 2 \end{array} \right|$
- Dઆમાંથી કોઈ નહીં
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જો $\left|\begin{array}{lll}x+1 & x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c\end{array}\right|=0$ હોય,તો $a, b, c$ એ
MediumKCET 2009
View Solution$x$ ના કયા ભિન્ન મૂલ્યો માટે શ્રેણિક $A=\begin{bmatrix} 1 & 1 & x \\ 1 & x & 1 \\ x & 1 & 1 \end{bmatrix}$ નો વ્યસ્ત અસ્તિત્વ ધરાવતો નથી,તે મૂલ્યોનો સરવાળો શોધો.
સમીકરણ $\left| \begin{matrix} x & a & b \\ a & x & a \\ b & b & x \end{matrix} \right| = 0$ ના ઉકેલ(ઓ) છે:
જો શ્રેણિક $\begin{bmatrix} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{bmatrix} - x \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ અસામાન્ય (singular) હોય,તો $x$ ની કિંમતોનો સરવાળો કેટલો થાય?
નિશ્ચાયક $ \left|\begin{array}{cc}\cos 15^{\circ} & \sin 15^{\circ} \\ \sin 75^{\circ} & \cos 75^{\circ}\end{array}\right| $ ની કિંમત શોધો.
MediumKCET 2015
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