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QuestionWrite the system of equations as a vector equation and a matrix equation:
8x1−x2=102x1+9x2=23x1−x2=1 \begin{array}{l} 8 x_{1}-x_{2}=10 \\ 2 x_{1}+9 x_{2}=2 \\ 3 x_{1}-x_{2}=1 \end{array}

Studdy Solution

STEP 1

Assumptions1. The system of equations is given as 8x1−x=10x1+9x=3x1−x=1\begin{array}{l} 8 x_{1}-x_{}=10 \\ x_{1}+9 x_{}= \\ 3 x_{1}-x_{}=1 \end{array}. We need to write this system as a vector equation and a matrix equation.

STEP 2

Let's start with the vector equation. We can write the system as a vector equation by grouping the coefficients of x1x_{1} and x2x_{2} into one vector, and the constants into another vector.
[82]x1+[−19−1]x2=[1021]\begin{bmatrix}8 \\2 \\ \end{bmatrix} x_{1} + \begin{bmatrix} -1 \\9 \\ -1 \end{bmatrix} x_{2} = \begin{bmatrix}10 \\2 \\1 \end{bmatrix}So, the correct choice for the vector equation is B. x1[82]+x2[−19−1]=[1021]x_{1} \begin{bmatrix}8 \\2 \\ \end{bmatrix} + x_{2} \begin{bmatrix} -1 \\9 \\ -1 \end{bmatrix} = \begin{bmatrix}10 \\2 \\1 \end{bmatrix}

STEP 3

Now, let's write the system as a matrix equation. We can do this by putting the coefficients of x1x_{1} and x2x_{2} into a matrix, the variables into a vector, and the constants into another vector.
[8−1293−1][x1x2]=[1021]\begin{bmatrix}8 & -1 \\2 &9 \\3 & -1 \end{bmatrix} \begin{bmatrix} x_{1} \\ x_{2} \end{bmatrix} = \begin{bmatrix}10 \\2 \\1 \end{bmatrix}So, the correct choice for the matrix equation is B. [8−1293−1][x1x2]=[1021]\begin{bmatrix}8 & -1 \\2 &9 \\3 & -1 \end{bmatrix} \begin{bmatrix} x_{1} \\ x_{2} \end{bmatrix} = \begin{bmatrix}10 \\2 \\1 \end{bmatrix}

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