If one of the roots of $\begin{vmatrix}
3 &5 & x \\
7 & x & 7 \\
x & 5 & 3
\end{vmatrix} = 0 $ is -10,then the other roots are
- 44627
- 4 , 7
- 44629
- 3,4
The Correct Option is A
Solution and Explanation
3 &5 & x \\
7 & x & 7 \\
x & 5 & 3
\end{vmatrix} = 0 $
$\Rightarrow \ \ \ 3(3x - 35) - 5(21 - 7x) + x(35 - x^2) = 0 $
$\Rightarrow \ \ \ 9x - 105 - 105 + 35x + 35x - x^3 = 0 $
$\Rightarrow \ \ \ x^3 - 79x + 210 = 0 $
$\Rightarrow \ \ \ (x + 10) (x - 3) (x -7) = 0 $
$\Rightarrow \ \ \ x = -10, 3, 7 $
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Concepts Used:
Transpose of a Matrix
The matrix acquired by interchanging the rows and columns of the parent matrix is called the Transpose matrix. The transpose matrix is also defined as - “A Matrix which is formed by transposing all the rows of a given matrix into columns and vice-versa.”
The transpose matrix of A is represented by A’. It can be better understood by the given example:
Now, in Matrix A, the number of rows was 4 and the number of columns was 3 but, on taking the transpose of A we acquired A’ having 3 rows and 4 columns. Consequently, the vertical Matrix gets converted into Horizontal Matrix.
Hence, we can say if the matrix before transposing was a vertical matrix, it will be transposed to a horizontal matrix and vice-versa.
Read More: Transpose of a Matrix
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