Question

The reduced row echelon form of the augmented matrix of a system of equations is given. Find the solutions of the system.

[1. 0. 0. 3. 13]
[0. 1. 0. 0. -8]
[0. 0. 1. -2. 5]
[0. 0. 0. 0. 0]


OA. (13 - 3w,- 8,5+2w.w) for any real number w
OB. (13+3w,- 8,5-2w,w) for any real number w
OC. (13. - 8,5,0)
OD. No solution Click to select your answer.

Answer 1

The system of equations has infinite solutions expressed as (13 - 3w, -8, 5 + 2w, w) for any real number w, which corresponds to option A.

Step-by-step explanation:

The system of equations represented by the augmented matrix is as follows:

• x + 3w = 13
• y = -8
• z - 2w = 5
• 0 = 0 (This is a redundant equation which implies an infinite number of solutions.)

From the above equations, we can express the variables in terms of 'w', which is a free variable. Therefore, the solution set is:

x = 13 - 3w

y = -8

z = 5 + 2w

Expressing the solution as an ordered tuple, we obtain (13 - 3w, -8, 5 + 2w, w) for any real number w. This corresponds to choice A from the given options.