Question

Identify the augmented matrix for the system of equations.

3x-2y+5z=30
5x+4z=35
3y-2z=-4
a. [3 -2 5 │30]
[5 0 4 │35]
[0 3 -2 │-4]

b. [3 5 53│30]
[-2 -4 -2 │35]
[5 0 0 │-4]

c. [3 -2 5 │30]
[5 0 4 │35]
[3 0 -2 │-4]

d. [3 -2 5 │30]
[5 0 4 │35]
[3 -2 0 │-4]

Answer 1

The correct augmented matrix corresponding to the given system of equations is option (a), which is represented as [3 -2 5 | 30], [5 0 4 | 35], [0 3 -2 | -4].

Step-by-step explanation:

To identify the augmented matrix for the given system of equations, we translate each equation into a row of the matrix. The system of equations is:

3x - 2y + 5z = 30

5x + 0y + 4z = 35

0x + 3y - 2z = -4

The corresponding augmented matrix is then:

The first row corresponds to the coefficients of x, y, z in the first equation and the constant term, resulting in [3 -2 5 | 30].

The second row follows from the second equation, noting that there is no y-term, giving us [5 0 4 | 35].

The third row is obtained from the third equation where there is no x-term, leading to [0 3 -2 | -4].

Therefore, the correct augmented matrix option is:

[3 -2 5 | 30]

[5 0 4 | 35]

[0 3 -2 | -4]

So, the answer is option (a).