Question

2x + y - z = -8
2y + 3z = -6
-1/2x + y + z = -4


For the following matrix, which of the following matrix operations would result in a11 = 1?


Multiply row 2 by -1 and add it to row 1.

Multiply row 1 by - 1/2.

Multiply row 1 by 1/2.

Multiply row 3 by -4 and add it to row 1.

(please show your solution if possible & pls just type in the comments if unsure abt your answer.. thank you)

Answer 1

Answer:

Multiply row 1 by $\frac{1}{2}$.

Step-by-step explanation:

The augmented matrix of the system of linear equation is described below:

$\left[\begin{array}{cccc}2&1&-1&-8\\0&2&3&-6\\-\frac{1}{2} &1&1&-4\end{array}\right]$

Where $a_{11} = 2$, if we need to create $a_{11} = 1$, we need to multiply row 1 by $\frac{1}{2}$, that is to say:

$\left[\begin{array}{cccc}1&\frac{1}{2} &-\frac{1}{2} &-4\\0&2&3&-6\\-\frac{1}{2} &1&1&-4\end{array}\right]$

Hence, the correct answer is: Multiply row 1 by $\frac{1}{2}$.