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AP EAPCET 08-Jul-2022 Shift 2 Paper

Section: Mathematics

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Question : 5 of 160

Marks: +1, -0

The rank of the matrix

A=\begin{bmatrix}1 & -1 & 0 & -2\\-4 & 4 & 0 & 8\\-2 & 1 & 2 & 4\end{bmatrix}

is

1
0
3
2

Solution:

Given,

A=\begin{bmatrix}1 & -1 & 0 & -2\\-4 & 4 & 0 & 8\\-2 & 1 & 2 & 4\end{bmatrix}

Now we apply elementary transformations,

Applying

R_3 \rightarrow R_3 + 2R_1

and

R_2 \rightarrow R_2 + 4R_1

A=\begin{bmatrix}1 & -1 & 0 & -2\\0 & 0 & 0 & 0\\0 & -1 & 2 & 0\end{bmatrix}

Applying

R_2 \leftrightarrow R_3

,

A=\begin{bmatrix}1 & -1 & 0 & -2\\0 & -1 & 2 & 0\\0 & 0 & 0 & 0\end{bmatrix}

Matrix

A

is in row echelon form.

Number of non-zero rows

=2

hence, rank of matrix

A=2

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