Question

Kyle wrote a matrix to represent a system of equations. The matrix is shown below.
7 -3 1
3 2 1
| -6 -4 -
21
Which of the following describes the solution to the system of equations?
O
consistent
dependent
inconsistent
independent

Answer 1

Answer:this inconsistent because it decreases

Step-by-step explanation:

this inconsistent because it decreases

Answer 2

The solution to the system of equations are inconsistent.

What is system of equation?

"It is a finite set of equations for which we can find the common solution."

What is an augmented matrix?

• "It is a matrix of numbers in which each row represents the constants from one equation and each column represents all the coefficients for a single variable."
• "This matrix is used to represent system of equations."

For given question,

We have been given a matrix that represents the system of equations.

This means, we have been given an augmented matrix.

Consider the given matrix,

$A=\begin{bmatrix}7 & 3 &| -6 \\-3 & 2 &| -4 \\1 & 1 &~| -21\end{bmatrix}$

After reducing the coefficient matrix to the row echelon form we have,

$A=\begin{bmatrix}7 & 3 &| -6 \\0 & \frac{23}{7} &| \frac{-46}{7} \\0 & 0 &~| -19\end{bmatrix}$

This means, the rank of augmented matrix is 3.

And the coefficient matrix would be,

$B=\begin{bmatrix}7 & 3 \\-3 & 2\\1 & 1 \end{bmatrix}$

After reducing the coefficient matrix to the row echelon form we have,

$B=\begin{bmatrix}7 & 3 \\0 & \frac{23}{7} \\0 & 0\end{bmatrix}$

This means, the rank of coefficient matrix is 2.

We know, if the coefficient matrix and augmented matrix has the same rank then the system of equations is consistent.

Here,

rank of A ≠ rank of B

This means, the rank of coefficient matrix of not equal to the rank of augmented matrix.

Therefore, the solution to the system of equations are inconsistent.

Learn more about the system of equations here:

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