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AP EAPCET 07-Jul-2022 Shift 2 Paper

Section: Mathematics

Question : 5 of 160

Marks: +1, -0

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

Solution: 👈: Video Solution

Convert matrix into row echelon form.

\; \begin{bmatrix} 2 & 1 & 2 \\ 1 & 0 & 1 \\ 4 & 1 & 4 \end{bmatrix} \xrightarrow[ ]{R_1 \rightarrow R_1 - R_2} \begin{bmatrix} 1 & 1 & 1 \\ 1 & 0 & 1 \\ 4 & 1 & 4 \end{bmatrix}

\; \begin{bmatrix} 1 & 1 & 1 \\ 1 & 0 & 1 \\ 4 & 1 & 4 \end{bmatrix} \; \xrightarrow[R_3 \rightarrow R_3 - 4 R_1]{R_2 - R_1} \begin{bmatrix} 1 & 1 & 1 \\ 0 & -1 & 0 \\ 0 & -3 & 0 \end{bmatrix}

\; \begin{bmatrix} 1 & 1 & 1 \\ 0 & -1 & 0 \\ 0 & -3 & 0 \end{bmatrix}_{R_3 \rightarrow \left(-\frac{1}{3}\right) R_3}^{\xrightarrow[ ]{R_2 \rightarrow (-1) R_2}} \begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & 0 \\ 0 & 3 & 0 \end{bmatrix}

\; \begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & 0 \\ 0 & 3 & 0 \end{bmatrix} \xrightarrow[R_3 \rightarrow R_3 - R_2]{} \begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{bmatrix}

Number of non-zero rows is 2 .

\therefore

Rank of matrix is 2 .

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