Question

Determine the rank of A

Answer 1

Answer:

The rank of a matrix is the number of nonzero rows in the reduced matrix, so the rank is 3. option (C)

Step-by-step explanation:

Echelon Form : it is used to find the rank of matrix by reducing rows into zeros then the number of non zero rows is the rank of the matrix

$\left[\begin{array}{ccccc}1&-1&5&-2&2\\2&-2&-2&5&1\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right]$

apply row operations:

R₂= R₂ - 2 R₁

$\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right]$

R₃= R₃ -  R₁

$\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\-1&1&7&-7&1\end{array}\right]$

R₄ = R₄ +R₁

$\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&12&-9 &3\end{array}\right]$

R₄ = R₄ +R₃

$\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&0&0 &0\end{array}\right]$

we can clearly see that after performing row operations there are 3 non zero rows,

therefore the Rank of the given matrix is 3

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