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Q.find the inerse of the matrix using elimentary row transformation

Question

help me to find the answer I couldn't get the correct answer
Q find the inerse of the matrix using elimentary row
transformation

Ajanta Trivedi · Accepted Answer

we will start out with an augmented matrix with the matrix , we want to inverse on left side and the identity matrix on the right side:

$[\begin{matrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{matrix} | \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$

now we will apply the elementary row operation, until we get the identity matrix on right side:

interchange $R_{2} a n d R_{1}$

$[\begin{matrix} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 3 & 1 & 1 \end{matrix} | \begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}]$

now applying $R_{1} \to R_{1} - 2 R_{2} a n d R_{3} \to R_{3} - R_{2}$

$[\begin{matrix} 1 & 0 & - 1 \\ 0 & 1 & 2 \\ 3 & 0 & - 1 \end{matrix} | \begin{matrix} - 2 & 1 & 0 \\ 1 & 0 & 0 \\ - 1 & 0 & 1 \end{matrix}]$

now applying $R_{3} \to R_{3} - 3 R_{1}$

$[\begin{matrix} 1 & 0 & - 1 \\ 0 & 1 & 2 \\ 0 & 0 & 2 \end{matrix} | \begin{matrix} - 2 & 1 & 0 \\ 1 & 0 & 0 \\ 5 & - 3 & 1 \end{matrix}]$

applying $R_{2} \to R_{2} - R_{3}$

$[\begin{matrix} 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & 0 & 2 \end{matrix} | \begin{matrix} - 2 & 1 & 0 \\ - 4 & 3 & - 1 \\ 5 & - 3 & 1 \end{matrix}]$

again applying $R_{3} \to \frac{R_{3}}{2}$

$[\begin{matrix} 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix} | \begin{matrix} - 2 & 1 & 0 \\ - 4 & 3 & - 1 \\ \frac{5}{2} & - \frac{3}{2} & \frac{1}{2} \end{matrix}]$

applying $R_{1} \to R_{1} + R_{3}$

$[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix} | \begin{matrix} \frac{1}{2} & - \frac{1}{2} & \frac{1}{2} \\ - 4 & 3 & - 1 \\ \frac{5}{2} & - \frac{3}{2} & \frac{1}{2} \end{matrix}]$

since right side is an identity matrix now.

so the inverse of the given matrix is

$[\begin{matrix} \frac{1}{2} & - \frac{1}{2} & \frac{1}{2} \\ - 4 & 3 & - 1 \\ \frac{5}{2} & - \frac{3}{2} & \frac{1}{2} \end{matrix}]$

hope this helps you.

cheers!!

help me to find the answer I couldn't get the correct answer Q.find the inerse of the matrix using elimentary row transformation

help me to find the answer I couldn't get the correct answer

Q.find the inerse of the matrix using elimentary row transformation