Question

If A = (10 0) (0 5)then, find rank of
matrix A is​

Answer 1

Answer:

Answer will be 0

Step-by-step explanation:

I think it will help for you

Answer 2

Rank of Matrix A = 2

Given:

Matrix A = $\left[\begin{array}{cc}10&0\\0&5&\end{array}\right]$

To find:

The rank of matrix A  

Solution:

The Rank of Matrix

• The rank of matrix is the number of linearly independent rows or columns in a Matrix.

• In simple words it is explained as the number of non-zero rows or columns of  a matrix

Finding Rank of Matrix

• To find a Rank of Matrix we need to convert given matrix into a Echelon Form by suitable elementary operations

       like, $\left[\begin{array}{cc}a&0\\0&b\end{array}\right]$, $\left[\begin{array}{ccc}a&b&c\\0&0&d\\0&0&0\end{array}\right]$  etc.  

• Then the rank of matrix will be equals to number of non-zero rows or columns of a matrix  

Here given matrix A = $\left[\begin{array}{cc}10&0\\0&5&\end{array}\right]$

As we can see that the matrix A is already in Echelon Form

then Rank of matrix = Number of non-zero rows or columns = 2

Therefore,

Rank of Matrix A = 2

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