Question

Reduce the matrix 'A' to its normal form where A=(0 1 2 -2/4 0 2 6 /2 1 3 1) and hence find its rank
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Answer 1

Answer: The rank of the matrix is 2.

Given: A=(0 1 2 -2/4 0 2 6 /2 1 3 1)

To Find: The rank of the matrix.

Step-by-step explanation:

Step 1: The number of linearly independent rows or columns in the matrix is referred to as the matrix's rank. The rank of matrix A is indicated by the notation (A). When all of a matrix's elements are zero, the matrix is said to have rank zero. The dimension of the vector space produced by the matrix's columns is its rank. A matrix's rank cannot be more than the sum of its rows or columns. The null matrix has a rank of 0.

Step 2: Given matrix is

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

Swap the 1st and the 2nd rows

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

Eliminate elements in the 1st column under the 1st element

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

Eliminate elements in the 2nd column under the 2nd element

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

Calculate the number of linearly independent rows.

Hence, the rank of the matrix is 2.

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