Question:
$\Delta =\begin{vmatrix}
sin^2x & cos^2x & 1 \\[0.3em]
cos^2x &sin^2x & 1 \\[0.3em]
-10 & 12& 2 \end{vmatrix}$
$\Delta =\begin{vmatrix}
sin^2x & cos^2x & 1 \\[0.3em]
cos^2x &sin^2x & 1 \\[0.3em]
-10 & 12& 2 \end{vmatrix}$
Updated On: Jul 6, 2022
- 0
- $12 cos ^2x-10sin^2x-2$
- $12 sin ^2x-10cos^2x-2$
- 10 sin 2x
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The Correct Option is A
Solution and Explanation
Operate $C_1 + C_2$
$\Delta = \begin{vmatrix}1&cos^{2}x&1\\ 1&sin^{2}x&1\\ 2&12&2\end{vmatrix} = 0 $ [$\therefore \, C_1 , C_3$ are identical]
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Concepts Used:
Matrices
Matrix:
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.
The basic operations that can be performed on matrices are:
- Addition of Matrices - The addition of matrices addition can only be possible if the number of rows and columns of both the matrices are the same.
- Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
- Scalar Multiplication - The product of a matrix A with any number 'c' is obtained by multiplying every entry of the matrix A by c, is called scalar multiplication.
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- Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.