Answer with explanation:
Consider a vector having 4 elements
[tex]\left[\begin{array}{cccc}a_{1}&a_{2}&a_{3}&a_{4}\end{array}\right][/tex]
it's first and third elements are equal.
That is,
[tex]a_{1}=a_{4}[/tex]
[tex]\left[\begin{array}{cccc}a_{1}&a_{2}&a_{3}&a_{4}\end{array}\right]\\\\R_{1}\rightarrow R_{1}-R_{3} \\\\\text{or}\\\\R_{3}\rightarrow R_{3}-R_{1}\\\\\left[\begin{array}{cccc}0&a_{2}&a_{3}&a_{4}\end{array}\right]\text{or}\left[\begin{array}{cccc}a_{1}&a_{2}&0&a_{4}\end{array}\right][/tex]
So, Dimension of vector=3
