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 $
Top Questions on Transpose of a Matrix
- The inverse of the matrix \[ \begin{bmatrix} 1 & 0 & 0 \\ 3 & 3 & 3 \\ 5 & 2 & -1 \end{bmatrix} \] is:
- MHT CET - 2024
- Mathematics
- Transpose of a Matrix
- If \[ B = \begin{bmatrix} 3 & \alpha & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3 \end{bmatrix} \] is the adjoint of a 3x3 matrix \( A \) and \( |A| = 4 \), then \( \alpha \) is equal to:
- MHT CET - 2024
- Mathematics
- Transpose of a Matrix
- If \( A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix} \), then \( A^{-1} \) is:
- MHT CET - 2024
- Mathematics
- Transpose of a Matrix
- The variance of the following probability distribution is:
\[ \begin{array}{|c|c|} \hline x & P(X) \\ \hline 0 & \frac{9}{16} \\ 1 & \frac{3}{8} \\ 2 & \frac{1}{16} \\ \hline \end{array} \]- MHT CET - 2024
- Mathematics
- Transpose of a Matrix
- The converse of \( ((\sim p) \land q) \Rightarrow r \) is:
- MHT CET - 2024
- Mathematics
- Transpose of a Matrix
Questions Asked in BITSAT exam
A particle is moving in a straight line. The variation of position $ x $ as a function of time $ t $ is given as:
$ x = t^3 - 6t^2 + 20t + 15 $.
The velocity of the body when its acceleration becomes zero is:- BITSAT - 2024
- thermal properties of matter
Evaluate the following limit: $ \lim_{n \to \infty} \prod_{r=3}^n \frac{r^3 - 8}{r^3 + 8} $.
- BITSAT - 2024
- limits and derivatives
- What is X in the following reaction?
$CO + 2H_2 \xrightarrow{X} CH_3OH$- BITSAT - 2024
- The solid state
- Consider the following two propositions: $$ P_1: \neg (p \rightarrow \neg q) $$ $$ P_2: (p \wedge \neg q) \wedge ((\neg p) \vee q) $$ If the proposition $p \rightarrow ((\neg p) \vee q)$ is evaluated as FALSE, then:
- BITSAT - 2024
- Statements
In the given cycle ABCDA, the heat required for an ideal monoatomic gas will be:
- BITSAT - 2024
- specific heat capacity
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