Question

Two augmented matrices for two linear systems in the variables x, y, and I are given below.

Answer 1

a) The system has infinitely many solutions in the following format:

(2 + z, 5 - z, z).

b) The system has no solution.

How to obtain the number of solutions of each system?

To obtain the number of solutions of each system, the equations are built from the augmented matrix presented.

For item a, both sides of the matrix have one zero row, hence the system has infinitely many solutions, and the equations are given as follows:

• x - z = 2.

• y + z = 5.

Hence the solutions in terms of z are given as follows:

• x = 2 + z.

• y = 5 - z.

Thus the format of the solutions is of:

(2 + z, 5 - z, z).

For item b, the right side has three non-zero rows, while the left-side has two, meaning that it has no solutions.

This can be verified from the last line, as the equation would be of:

0z = -2.

Which has no solution.

More can be learned about a system of equations at brainly.com/question/24342899

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