Question

please help me

please help me​

Answer 1

GIVEN :–

• A matrix $\to\bf \: A = \left[ \begin{array}{cc} \: 1&2 \\ 4&3 \end{array}\right]$

• Ax = I

TO FIND :–

• x = ?

SOLUTION :–

$\\ \implies\bf \: Ax = I$

• Now put the values –

$\\ \implies\bf \: \left[ \begin{array}{cc} \: 1&2 \\ 4&3 \end{array}\right]x = \left[ \begin{array}{cc} \: 1&0\\ 0&1 \end{array}\right]$

• Now let's apply operations –

$\\ \longrightarrow \: \: \bf \: R_2 = R_2 - 4R_1$

$\\ \implies\bf \: \left[ \begin{array}{cc} \: 1&2 \\ 0& - 5 \end{array}\right]x = \left[ \begin{array}{cc} \: 1&0\\ - 4&1 \end{array}\right]$

$\\ \longrightarrow \: \: \bf \: R_2 = \dfrac{R_2}{ - 5}$

$\\ \implies\bf \: \left[ \begin{array}{cc} \: 1&2 \\ 0& 1 \end{array}\right]x = \left[ \begin{array}{cc} \: 1&0\\ \dfrac{4}{5}& - \dfrac{1}{5} \end{array}\right]$

$\\ \longrightarrow \: \: \bf \: R_1 = R_1 - 2R_2$

$\\ \implies\bf \: \left[ \begin{array}{cc} \: 1&0 \\ 0& 1 \end{array}\right]x = \left[ \begin{array}{cc} \: - \dfrac{3}{5}&\dfrac{2}{5}\\ \\ \dfrac{4}{5}& - \dfrac{1}{5} \end{array}\right]$

$\\ \implies\bf \: Ix = \left[ \begin{array}{cc} \: - \dfrac{3}{5}&\dfrac{2}{5}\\ \\ \dfrac{4}{5}& - \dfrac{1}{5} \end{array}\right]$

$\\ \implies\bf \: x = \left[ \begin{array}{cc} \: - \dfrac{3}{5}&\dfrac{2}{5}\\ \\ \dfrac{4}{5}& - \dfrac{1}{5} \end{array}\right]$

$\\ \implies\bf \: x = \dfrac{1}{5} \left[ \begin{array}{cc} \: - 3&2\\ \\ 4& - 1 \end{array}\right]$

• Hence , Option (c) is correct.