Question

0-3 Reduce the matrix I to normal form and hence find its rank, A = 5 3 8 0 1 1 0 1 1​

Answer 1

Answer:

hdjdnr.7884

Step-by-step explanation:

rank a.

46(. 7474) √ (√ 38 )783i3o4

4484

44

494

4

4k4

4944

Answer 2

Given,

The matrix $\left[\begin{array}{ccc}5&3&8\\0&1&1\\0&1&1\end{array}\right]$ is given.

To find,

We have to find the normal form of the given matrix and its rank.

Solution,

The normal form of matrix 'I' is $\left[\begin{array}{ccc}I2&0\\0&0\0\end{array}\right]$ and its rank is 2.

We can simply find the normal form of I and its rank using elementary row and column operations.

    I =   $\left[\begin{array}{ccc}5&3&8\\0&1&1\\0&1&1\end{array}\right]$

   Using  R₃ → R₃ - R₂

   I = $\left[\begin{array}{ccc}5&3&8\\0&1&1\\0&0&0\end{array}\right]$

   Using C₃ → C₃ - C₂

   I = $\left[\begin{array}{ccc}5&3&5\\0&1&0\\0&0&0\end{array}\right]$

   Using R₁ → R₁ / 5

  I = $\left[\begin{array}{ccc}1&3/5&1\\0&1&0\\0&0&0\end{array}\right]$

   Using C₃ → C₃ - C₁

  I = $\left[\begin{array}{ccc}1&3/5&0\\0&1&0\\0&0&0\end{array}\right]$

   Using C₂ → C₂ - (3/5)C₁

  I = $\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&0\end{array}\right]$

Since there are two non-zero rows in the matrix I so the rank of matrix 'I' is 2.

I = $\left[\begin{array}{ccc}I2&0\\0&0\0\end{array}\right]$

The above-given form is the normal form of the matrix 'I'.

Hence, the normal form of matrix 'I' is $\left[\begin{array}{ccc}I2&0\\0&0\0\end{array}\right]$ and its rank is 2.