Question

The augmented matrix that represents the system of questions below would have which of the following dimensions?

4x + 2y = 7
5y = 10

Answer 1

The dimensions of the augmented matrix for the given system of equations are 2x3, representing two rows for each equation and three columns for the two variables x and y, plus the constant terms.

Step-by-step explanation:

To determine the dimensions of the augmented matrix for the system of equations given as:

1. 4x + 2y = 7
2. 5y = 10

First, we convert the system of equations to an augmented matrix. Each equation will correspond to a row in the matrix, and each variable and the constant term will correspond to a column. In our case, we have two variables (x and y) and the constant term that will be on the other side of the partition.

Therefore, the augmented matrix will be:

[4 2 | 7]
[0 5 | 10]

This results in a matrix with 2 rows and 3 columns (since the constant term counts as a column in the augmented matrix).

The dimensions of the augmented matrix are thus 2x3.