Questions: Write the system first as a vector equation and then as a matrix equation. 2 x1+x2-3 x3=2 7 x2+33=0 Write the system as a vector equation where the first equation of the system corresponds to the first row. Select the correct choice below and fill in any answer boxes to complete your choice. A. x1 +x2 +x3 B. [x1 x2 x3] = C. [x1 x2 x3] =

Solution Steps

To convert the given system of equations into a vector equation, we need to express the system in terms of vectors and matrices. The first step is to identify the coefficients of the variables in each equation and represent them as vectors. Then, we can express the system as a matrix equation by organizing these vectors into a matrix and equating it to a result vector.

We are given a system of linear equations and need to express it first as a vector equation and then as a matrix equation. The system of equations is:

\[ \begin{array}{r} 2x_{1} + x_{2} - 3x_{3} = 2 \\ 7x_{2} + 33 = 0 \end{array} \]

A vector equation expresses the system in terms of vectors and their linear combinations. The given system can be written as:

\[ 2x_{1} + x_{2} - 3x_{3} = 2 \]

\[ 0x_{1} + 7x_{2} + 0x_{3} = -33 \]

This can be expressed as:

\[ \begin{bmatrix} 2 \\ 0 \end{bmatrix} x_1 + \begin{bmatrix} 1 \\ 7 \end{bmatrix} x_2 + \begin{bmatrix} -3 \\ 0 \end{bmatrix} x_3 = \begin{bmatrix} 2 \\ -33 \end{bmatrix} \]

A matrix equation expresses the system in the form \( A\mathbf{x} = \mathbf{b} \), where \( A \) is the coefficient matrix, \( \mathbf{x} \) is the vector of variables, and \( \mathbf{b} \) is the constant vector.

The matrix equation for the given system is:

\[ \begin{bmatrix} 2 & 1 & -3 \\ 0 & 7 & 0 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 2 \\ -33 \end{bmatrix} \]

Final Answer