જો $\left| \begin{array}{ccc} x - 1 & 3 & 0 \\ 2 & x - 3 & 4 \\ 3 & 5 & 6 \end{array} \right| = 0$ હોય,તો $x =$

  • A
    $0$
  • B
    $2$
  • C
    $3$
  • D
    $1$

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ધારો કે $A = \begin{bmatrix} 3-t & 1 & 0 \\ -1 & 3-t & 1 \\ 0 & -1 & 0 \end{bmatrix}$ અને $\det(A) = 5$ છે, તો $t$ ની કિંમત શોધો.

જો $\left| {\begin{array}{*{20}{c}}{y + z}&{x - z}&{x - y}\\{y - z}&{z + x}&{y - x}\\{z - y}&{z - x}&{x + y}\end{array}} \right| = kxyz$ હોય,તો $k$ ની કિંમત શોધો.

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.

જો $A, B, C$ એ ત્રિકોણના ખૂણાઓ હોય,તો સમીકરણોની સંહતિ $-x + y \cos C + z \cos B = 0$,$x \cos C - y + z \cos A = 0$,$x \cos B + y \cos A - z = 0$ ધરાવે છે

જો $w = \frac{-1-i \sqrt{3}}{2}$ જ્યાં $i = \sqrt{-1}$ હોય,તો $\left|\begin{array}{ccc}1 & w & w^2 \\ w & w^2 & 1 \\ w^2 & 1 & w\end{array}\right|$ નું મૂલ્ય શોધો.

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