Class 12 Mathematics 3-4. Matrices and Determinants Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

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જો $\left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|=\left|\begin{array}{ll}x & 3 \\ 2x & 5\end{array}\right|$ હોય,તો $x$ ની કિંમત શોધો.

A
$x=2$
B
$x=3$
C
$x=4$
D
$x=5$

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Class 12

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3-4. Matrices and Determinants

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Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

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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.

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જો $A_{\lambda} = \begin{bmatrix} \lambda & \lambda - 1 \\ \lambda - 1 & \lambda \end{bmatrix}; \lambda \in N$ હોય,તો $|A_1| + |A_2| + \dots + |A_{300}|$ ની કિંમત શોધો.

$\left|\begin{array}{ccc}a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b\end{array}\right|=$ નું મૂલ્ય શું છે?

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આપેલ સમીકરણ સંહતિ $a(x + y + z) = x$,$b(x + y + z) = y$,$c(x + y + z) = z$ માટે જ્યાં $a, b, c$ એ શૂન્યતર વાસ્તવિક સંખ્યાઓ છે. જો વાસ્તવિક સંખ્યાઓ $x, y, z$ એવી હોય કે $xyz \neq 0$,તો $(a + b + c)$ ની કિંમત કેટલી થાય?

જો $\left|\begin{array}{lll}3 & 5 & x \\ 7 & x & 7 \\ x & 5 & 3\end{array}\right|=0$ ના બીજ પૈકીનું એક બીજ $-10$ હોય, તો અન્ય બીજ કયા છે?

EasyAP EAMCET 2009

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