Math, asked by shaikismathkhaja, 18 days ago

Find the rank of
-1,-2,-3
3,4,5
4,5,6

Answers

Answered by padmavathikoduru18
0

Answer:

0 is the rank of given number

Answered by mathdude500
3

\large\underline{\sf{Solution-}}

Given matrix is

\begin{gathered}\sf\left[\begin{array}{ccc} - 1&-2& -3\\3&4&5\\4&5&6\end{array}\right]\end{gathered} \\

Let assume that

 \:  \:  \:  \qquad \quad\rm \: A \:  =  \: \begin{gathered}\sf\left[\begin{array}{ccc} - 1&-2& -3\\3&4&5\\4&5&6\end{array}\right]\end{gathered} \\

 \:  \:  \:  \qquad \quad \red{\boxed{ \sf{ \:OP \: R_3 \:  \to \:  \: R_3  -  R_2 \:  \: }} }\\

 \:  \:  \:  \qquad \quad\rm \:  =  \: \begin{gathered}\sf\left[\begin{array}{ccc} - 1&-2& -3\\3&4&5\\1&1&1\end{array}\right]\end{gathered} \\

 \:  \:  \:  \qquad \quad \red{\boxed{ \sf{ \:OP \: R_3 \:  \to \:  \: R_3 + R_1 \:  \: }} }\\

 \:  \:  \:  \qquad \quad\rm \:  =  \: \begin{gathered}\sf\left[\begin{array}{ccc} - 1&-2& -3\\3&4&5\\0& - 1& - 2\end{array}\right]\end{gathered} \\

 \:  \:  \:  \qquad \quad \red{\boxed{ \sf{ \:OP \: R_2 \:  \to \:  \: R_2+ 3R_1\:  \: }} }\\

 \:  \:  \:  \qquad \quad\rm \:  =  \: \begin{gathered}\sf\left[\begin{array}{ccc} - 1&-2& -3\\0& - 2& - 4\\0& - 1& - 2\end{array}\right]\end{gathered} \\

 \:  \:  \:  \qquad \quad \red{\boxed{ \sf{ \:OP \: R_2 \:  \to \:  \: -   \frac{1}{2} R_2\:  \: }} }\\

 \:  \:  \:  \qquad \quad\rm \:  =  \: \begin{gathered}\sf\left[\begin{array}{ccc} - 1&-2& -3\\0& 1& 2\\0& - 1& - 2\end{array}\right]\end{gathered} \\

 \:  \:  \:  \qquad \quad \red{\boxed{ \sf{ \:OP \: R_3 \:  \to \:  \: R_3   +   R_2 \:  \: }} }\\

 \:  \:  \:  \qquad \quad\rm \:  =  \: \begin{gathered}\sf\left[\begin{array}{ccc} - 1&-2& -3\\0&1&2\\0&0&0\end{array}\right]\end{gathered} \\

Since, number of non - zero rows is 2.

\bf\implies \: \rho \: (A) \:  =  \: 2 \\

Similar questions