Respuesta :
Answer: The required matrix A is
[tex]A=\left[\begin{array}{ccc}4&5&2\\5&1&0\\2&0&3\end{array}\right] .[/tex]
Step-by-step explanation: We are given to write a 3 × 3 symmetric matrix A that has entries as follows :
[tex]a_{11}=4,~~a_{22}=1,~~a_{33}=3,~~a_{21}=5,~~a_{13}=2,~~a_{23}=0.[/tex]
We know that in a symmetric matrix,
[tex]a_{ij}=a_{ji},~i\neq j.[/tex]
Since A is a 3 × 3 symmetric matrix, so we must have
[tex]a_{12}=a_{21}=5,\\\\a_{13}=a_{31}=2,\\\\a_{23}=a_{32}=0.[/tex]
Therefore, the 3 × 3 symmetric matrix A is written as follows :
[tex]A=\left[\begin{array}{ccc}4&5&2\\5&1&0\\2&0&3\end{array}\right] .[/tex]
Thus, the required matrix A is
[tex]A=\left[\begin{array}{ccc}4&5&2\\5&1&0\\2&0&3\end{array}\right] .[/tex]
Using the concept of symmetry, the matrix is given by:
[tex]M = \left[\begin{array}{ccc}4&5&2\\5&1&0\\2&0&3\end{array}\right][/tex]
A 3x3 matrix is given by:
[tex]M = \left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{32}\\a_{31}&a_{32}&a_{33}\end{array}\right][/tex]
The symmetry means that:
[tex]a_{ij} = a_{ji}[/tex]
Then:
[tex]a_{11} = 4[/tex]
[tex]a_{22} = 1[/tex]
[tex]a_{33} = 3[/tex]
[tex]a_{21} = a_{12} = 5[/tex]
[tex]a_{13} = a_{31} = 2[/tex]
[tex]a_{23} = a_{32} = 0[/tex]
Which means that the matrix is:
[tex]M = \left[\begin{array}{ccc}4&5&2\\5&1&0\\2&0&3\end{array}\right][/tex]
A similar problem is given at https://brainly.com/question/13266649
