Question

Find the rank of the matrix

A= (8001 1081 0018 0118)

Answer 1

Answer:

The rank of the matrix is 4.

Step-by-step explanation:

Consider the provided matrix.

The rank of a matrix is the number of non all-zeros rows

Maximum number of linearly independent column vectors in the matrix is known as the rank of a matrix.

Reduce matrix to reduced row echelon form:

Perform $R_2\:\leftarrow \:R_2-\frac{1}{8}\cdot \:R_1$

$\begin{pmatrix}8&0&0&1\\ 0&0&8&\frac{7}{8}\\ 0&0&1&8\\ 0&1&1&8\end{pmatrix}$

$R_2\:\leftrightarrow \:R_4$

$\begin{pmatrix}8&0&0&1\\ 0&1&1&8\\ 0&0&1&8\\ 0&0&8&\frac{7}{8}\end{pmatrix}$

$R_3\:\leftrightarrow \:R_4$

$\begin{pmatrix}8&0&0&1\\ 0&1&1&8\\ 0&0&8&\frac{7}{8}\\ 0&0&1&8\end{pmatrix}$

$R_4\:\leftarrow \:R_4-\frac{1}{8}\cdot \:R_3$

$\begin{pmatrix}8&0&0&1\\ 0&1&1&8\\ 0&0&8&\frac{7}{8}\\ 0&0&0&\frac{505}{64}\end{pmatrix}$

Hence, the rank of the matrix is 4.

Answer 2

Answer:

Rank of matrix=4

Step-by-step explanation:

We are given that a matrix

A=$\left[\begin{array}{cccc}8&0&0&1\\1&0&8&1\\0&0&1&8\\0&1&1&8\end{array}\right]$

We have to find the rank of  matrix

Apply $R_4\rightarrow R_4-R_3$

Then, we get

$\left[\begin{array}{cccc}8&0&0&1\\1&0&8&1\\0&0&1&8\\0&1&0&0\end{array}\right]$

Apply $R_2\rightarrow R_2-8R_3$

Then , we get

$\left[\begin{array}{cccc}8&0&0&1\\1&0&0&-63\\0&0&1&8\\0&1&0&0\end{array}\right]$

Apply $R__1\rightarrow R_1-8R_2$

$\left[\begin{array}{cccc}0&0&0&505\\1&0&8&-63\\0&0&1&8\\0&1&0&0\end{array}\right]$

Appiy $C_3\rightarrow C_3-8C_1$

$\left[\begin{array}{cccc}0&0&0&505\\1&0&0&-63\\0&0&1&8\\0&1&0&0\end{array}\right]$

Number of non zeroes rows=4

Hence, the rank of matrix=4