Question

The linear system below represents the sales of large and small popcorn servings at a movie theater for two consecutive days.

Answer 1

2 X 3
the rows are listed first (2) and the columns (3) are listed second because they share all of the same variables the system does not need to be spread out further than it is currently listed.

Answer 2

The size of the augmented matrix for this system is:

2×3

Explanation:

We are given a system of linear equation consisting of two variables L and S as:

`42L+61S=\$ 393\\\\59L+78S=\$ 529`

Hence, the system that is formed is:

`AX=b`

where
`A=\left[\begin{array}{ccc}42&61\\59&78\end{array}\right]`

`X=\left[\begin{array}{ccc}L\\S\end{array}\right]`

and

`b=\left[\begin{array}{ccc}393\\529\end{array}\right]`

and the augmented matrix is written as:

`Aug\ A=\left[\begin{array}{ccc}42&61&393\\59&78&529\end{array}\right]`

Hence, the size of the augmented matrix for this system is:

2×3