Question

[tex] If D=\left|\begin{array}{ccc}2&3&1\\5&-1&2\\7&4&-1\end{array}\right|,

performing R₁₂(-1) on D; then D will become.............,Select Proper option from the given options.

\left|\begin{array}{ccc}-1&3&1\\6&-1&2\\3&4&-1\end{array}\right|

\left|\begin{array}{ccc}2&1&1\\5&-6&2\\7&-3&-1\end{array}\right|

\left|\begin{array}{ccc}-3&4&-1\\5&-1&2\\7&4&-1\end{array}\right|

\left|\begin{array}{ccc}2&3&1\\3&-4&1\\7&4&-1\end{array}\right|
[/tex]

Answer 1

Answer:

After performing $R_{12}(-1)$ on $D$ it will become

$\left[\begin{array}{ccc}-3&4&-1\\5&-1&2\\7&4&-1\end{array}\right]$

Step-by-step explanation:

I think with $R_{12}(-1)$ you are referring to the matrix row operation $R_1 \rightarrow R_1+(-1) R_2$.

In this case, you have

$R_1 \rightarrow R_1+(-1) R_2 = (2,3,1)-(5,-1,2) = (-3, 4, -1)$

So the matrix $D$ becomes

$\left[\begin{array}{ccc}-3&4&-1\\5&-1&2\\7&4&-1\end{array}\right]$