Class 12Mathematics3-4. Matrices and DeterminantsExpansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line
Easyધારો કે $A = \begin{bmatrix} x+2 & 3x \\ 3 & x+2 \end{bmatrix}$ અને $B = \begin{bmatrix} x & 0 \\ 5 & x+2 \end{bmatrix}$ છે. તો સમીકરણ $\det(AB) = 0$ ના તમામ ઉકેલો શોધો.
- A$1, -1, 0, 2$
- B$1, 4, 0, -2$
- C$1, -1, 4, 3$
- D$-1, 4, 0, 3$
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Similar Questions
જો $f(x) = \left| \begin{array}{ccc} 1 & x & x + 1 \\ 2x & x(x - 1) & (x + 1)x \\ 3x(x - 1) & x(x - 1)(x - 2) & (x + 1)x(x - 1) \end{array} \right|$ હોય,તો $f(100)$ ની કિંમત શોધો.
DifficultIIT 1999
View Solutionજો નીચેના ત્રણ સુરેખ સમીકરણોનો બિન-તુચ્છ ઉકેલ હોય, તો
$x+4ay+az=0$
$x+3by+bz=0$
$x+2cy+cz=0$
$x+4ay+az=0$
$x+3by+bz=0$
$x+2cy+cz=0$
જો $\left| {\begin{array}{*{20}{c}}{\cos (A + B)}&{ - \sin (A + B)}&{\cos 2B}\\{\sin A}&{\cos A}&{\sin B}\\{ - \cos A}&{\sin A}&{\cos B}\end{array}} \right| = 0$ હોય,તો $B =$
Medium
View Solutionજો $a, b$ અને $c$ વાસ્તવિક સંખ્યાઓ હોય,અને $\Delta=\begin{vmatrix} b+c & c+a & a+b \\ c+a & a+b & b+c \\ a+b & b+c & c+a \end{vmatrix}=0$ હોય,તો સાબિત કરો કે $a+b+c=0$ અથવા $a=b=c$.
Difficult
View Solutionજો $\alpha \neq a, \beta \neq b, \gamma \neq c$ અને $\left|\begin{array}{lll}\alpha & b & c \\ a & \beta & c \\ a & b & \gamma\end{array}\right|=0$ હોય,તો $\frac{a}{\alpha-a}+\frac{b}{\beta-b}+\frac{\gamma}{\gamma-c}$ ની કિંમત શોધો:
DifficultJEE MAIN 2024
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