Question

रैंक आफ ए मैट्रिक्स​

Answer 1

Answer:

Rank = 3

Step-by-step explanation:

apply $R_{1}$ → $R_{1}$ / 2

$\left[\begin{array}{cccc}1&1.5&-0.5&-0.5\\1&-1&-2&-4\\3&1&3&-4\\6&3&0&-7\end{array}\right]$

apply  $R_{2}$ → $R_{2}$ -  $R_{1}$ , $R_{3}$  → $R_{3}$ - 3$R_{1}$ , $R_{4}$ →  $R_{4}$ - 6$R_{1}$

$\left[\begin{array}{cccc}1&1.5&-0.5&-0.5\\0& -2.5 &-1.5& -3.5\\0 &-3.5& 4.5& -0.5\\0&-6 &3 &-4\end{array}\right]$

apply $R_{2}$ → $R_{2}$ / -2.5

$\left[\begin{array}{cccc}1&1.5&-0.5&-0.5\\0 &1& 0.6& 1.4\\0 &-3.5& 4.5& -0.5\\0&-6 &3 &-4\end{array}\right]$

apply  $R_{3}$ → $R_{3}$ + 3.5 $R_{2}$

$\left[\begin{array}{cccc}1&1.5&-0.5&-0.5\\0 &1& 0.6& 1.4\\0& 0& 6.6 &4.4\\0& 0& 6.6 &4.4\end{array}\right]$

apply $R_{3}$ → $R_{3}$ / 6.6

$\left[\begin{array}{cccc}1&1.5&-0.5&-0.5\\0 &1& 0.6& 1.4\\0&0&1&2/3\\0& 0& 6.6 &4.4\end{array}\right]$

apply $R_{4}$  →  $R_{4}$ - 6.6$R_{3}$

$\left[\begin{array}{cccc}1&1.5&-0.5&-0.5\\0 &1& 0.6& 1.4\\0&0&1&2/3\\0& 0& 0 &0\end{array}\right]$

Since there is 3 non-zero rows, then Rank(A) = 3.