Find the set of solutions for the linear system.

-3x_1 - x_2 + 4x_3 = 2

-3x_3 - 4x_4 = -1

Use s1, s2, etc. for the free variables if necessary.

The system has infinitely many solutions.

Step-by-step explanation:

To find the solution for this system of linear equations you must:

Step 1: Transform the augmented matrix to the reduced row echelon form.

A matrix is a rectangular arrangement of numbers into rows and columns.

A system of equations can be represented by an augmented matrix.

In an augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

This is matrix that represents the system

The augmented matrix can be transformed by a sequence of elementary row operations to the matrix.

There are three kinds of elementary matrix operations.

Using elementary matrix operations, we get that

Row Operation 1: Multiply the 1st row by -1/3

Row Operation 2: Multiply the 2nd row by -1/3

Row Operation 3: Add 4/3 times the 2nd row to the 1st row

Step 2: Interpret the reduced row echelon form

The reduced row echelon form of the augmented matrix is

which corresponds to the system

We see that the variables can take arbitrary numbers; they are called free variables. Let , . All solutions of the system are given by

The system has infinitely many solutions.

it is b)

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step-by-step explanation:

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step-by-step explanation: