Question

Write the system first as a vector equation and then as a matrix equation. 4x1- x2 = 6 2x110x2 2 6x1- X2=1 Write the system as a vector equation. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. X2 Write the system first as a vector equation and then as a matrix equation. 4x1- x2 = 6 2x110x2 - 2 6X1- X2=1 Write the system as a matrix equation. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choic X1X2ー X2 Click to select and enter your answer(s).

Answer 1

Answer):

We can define two vectors $\vec{x}_1, \vec{x}_2$ which are defined such that the components represent which equation we are looking at. Then the first equation can be cast as:

$\begin{bmatrix} 4\\ 2\\ 6 \end{bmatrix} \vec{x}_1 + \begin{bmatrix} -1\\ 10\\ -1 \end{bmatrix} \vec{x}_2 = \begin{bmatrix} 6\\ 2\\ 1 \end{bmatrix}$

in the form of a vector equation, and each component gives us one equation in the original formulation. Hence, option C would be correct answer.

Similarly, we would arrange the given equations in matrix format as follows:

2 0 1

Here, each row of the multiplied out matrix on the left hand side gives us one equation in the original formulation. Hence, option B is the right choice, with the above matrix filled in the blank.