Question

If A= matrix [ 2 1 1 1 0 1 0 2 -1],find the inverse of A using elementary row transformations and hence solve the following matrix equation XA=[1 0 1].
Please explain and answer the question.​

Answer 1

Given :    A  =  $\left[\begin{array}{ccc}2&1&1\\1&0&1\\0&2&-1\end{array}\right]$

To find : inverse of A using elementary row transformations

Solution:

A  =  IA

& I  = A⁻¹A

$\left[\begin{array}{ccc}2&1&1\\1&0&1\\0&2&-1\end{array}\right]$   =   $\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] A$

R₁  → R₁ - R₂

$\left[\begin{array}{ccc}1&1&0\\1&0&1\\0&2&-1\end{array}\right] = \left[\begin{array}{ccc}1&-1&0\\0&1&0\\0&0&1\end{array}\right] A$

R₂  → R₂ + R₃ - R₁

$\left[\begin{array}{ccc}1&1&0\\0&1&0\\0&2&-1\end{array}\right] = \left[\begin{array}{ccc}1&-1&0\\-1&2&1\\0&0&1\end{array}\right] A$

R₁  → R₁ - R₂

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&2&-1\end{array}\right] = \left[\begin{array}{ccc}2&-3&-1\\-1&2&1\\0&0&1\end{array}\right] A$

R₃ → R₃ - 2R₂  

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&-1\end{array}\right] = \left[\begin{array}{ccc}2&-3&-10\\-1&2&1\\2&-4&-1\end{array}\right] A$

R₃ → R₃ * - 1

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] = \left[\begin{array}{ccc}2&-3&-10\\-1&2&1\\-2&4&1\end{array}\right] A$

A⁻¹ = $\left[\begin{array}{ccc}2&-3&-10\\-1&2&1\\-2&4&1\end{array}\right]$

Learn More:

If a=matrix 2,3,5,-2 write a inverse in terms of a - Brainly.in

https://brainly.in/question/3109606

A dealer purchased refrigerator of 11515 and allows discount of 16 ...

https://brainly.in/question/7359848