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# Determinants

At Saralstudy, we are providing you with the solution of Class 12th mathematics Determinants according to the latest NCERT (CBSE) Book guidelines prepared by expert teachers. Here we are trying to give you a detailed answer to the questions of the entire topic of this chapter so that you can get more marks in your examinations by preparing the answers based on this lesson. We are trying our best to give you detailed answers to all the questions of all the topics of Class 12th mathematics Determinants so that you can prepare for the exam according to your own pace and your speed.

Determinant is a continuation of the previous chapter matrix. Matrix and determinant are the core topics of algebra. These will help us to solve many algebraic linear equations very easily. Matrix and determinants both are interlinked. Topics which are covered in this chapter - determinant of a square matrix (upto 3x3), minors. cofactors, finding the area of triangle, adjoint and inverse of square matrix, consistency & inconsistency and number of solutions of system of linear equation, solving system of linear equation in two or three variables using inverse of a matrix.

•  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) $$\begin{vmatrix}2 & 3\\4 & 5\end{vmatrix}$$ = $$\begin{vmatrix}x & 3\\2x & 5\end{vmatrix}$$