Determinants Free CBSE NCERT solution for class 12th mathematics

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Q1	Evaluate the determinants \begin{vmatrix} \mathbf{2} & \mathbf{4} \\ \mathbf{-5} & \mathbf{-1} \end{vmatrix}
Q2	Evaluate the determinants (i) \begin{vmatrix} \mathbf{Cosθ} & \mathbf{−sin θ} \\ \mathbf{sin θ} & \mathbf{cos θ} \end{vmatrix} (ii) \begin{vmatrix} \mathbf{x^2 − x + 1} & \mathbf{x − 1} \\ \mathbf{x + 1} & \mathbf{x + 1} \end{vmatrix}
Q3	If A=\(\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}\), then show that \|2A\| = 4\|A\|
Q4	If A=\(\begin{bmatrix}1 & 0 & 1\\0 & 1 & 2\\0 & 0 & 4\end{bmatrix}\), then show that \|3A\| = 27\|A\|.
Q5	Evaluate the determinants (i) \(\begin{vmatrix}3 & -1 & -2\\0 & 1 & 2\\0 & 0 & 4\end{vmatrix}\) (iii) \(\begin{vmatrix}3 & -4 & 5\\1 & 1 & -2\\2 & 3 & 1\end{vmatrix}\) (ii) \(\begin{vmatrix}0 & 1 & 2\\-1 & 0 & -3\\-2 & 3 & 0\end{vmatrix}\)(iv) \(\begin{vmatrix}2 & -1 & -2\\0 & 2 & -1\\3 & -5 & 0\end{vmatrix}\)
Q6	If A = \(\begin{bmatrix}1 & 1 & -2\\2 & 1 & -3\\5 & 4 & -9\end{bmatrix}\), Find \|A\|
Q7	Find values of x, if (i) \(\begin{vmatrix}2 & 4\\2 & 1\end{vmatrix}\) = \(\begin{vmatrix}2x & 4\\6 & x\end{vmatrix}\) (ii) \(\begin{vmatrix}2 & 3\\4 & 5\end{vmatrix}\) = \(\begin{vmatrix}x & 3\\2x & 5\end{vmatrix}\)