Matrix Representation of Linear Equations: CCSS.Math.Content.HSA-REI.C.8 - Common Core: High School - Algebra

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Question

Put the equations into proper matrix form.

Answer

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} a \ b \ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -29 & -30 & 36 \ -14 & 48 & 35 \ -23 & 19 & -43 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -37 \ -37 \ 36 \end{bmatrix}$

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Question

Put the equations into proper matrix form.

Answer

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} a \ b \ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -5 & 12 & 35 \ 3 & -13 & -6 \ 48 & 15 & 44 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 0 \ 9 \ 35 \end{bmatrix}$

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Question

Put the equations into proper matrix form.

Answer

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} a \ b \ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} 44 & -5 & 33 \ 40 & 18 & -28 \ 18 & -18 & -1 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -1 \ -8 \ 33 \end{bmatrix}$

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Question

Put the equations into proper matrix form.

Answer

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} a \ b \ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -37 & -43 & 33 \ 34 & -29 & 2 \ -14 & 27 & 35 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 13 \ -6 \ 33 \end{bmatrix}$

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Question

Put the equations into proper matrix form.

Answer

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} a \ b \ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -34 & 29 & -19 \ -48 & 9 & -13 \ -47 & 37 & -3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 40 \ 30 \ -19 \end{bmatrix}$

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Question

Put the equations into proper matrix form.

Answer

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} a \ b \ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -47 & 3 & 37 \ 18 & 37 & -27 \ 31 & -20 & 29 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 2 \ 42 \ 37 \end{bmatrix}$

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Question

Put the equations into proper matrix form.

Answer

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} a \ b \ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -46 & 10 & 19 \ -11 & -16 & 49 \ 13 & -35 & -46 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -3 \ -31 \ 19 \end{bmatrix}$

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Question

Put the equations into proper matrix form.

Answer

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} a \ b \ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} 39 & 34 & -35 \ 16 & 7 & 31 \ -48 & 29 & 44 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 2 \ -44 \ -35 \end{bmatrix}$

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Question

Put the equations into proper matrix form.

Answer

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} a \ b \ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -31 & -26 & -48 \ 4 & 42 & -12 \ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 19 \ 35 \ -48 \end{bmatrix}$

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Question

Put the equations into proper matrix form.

Answer

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} a \ b \ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -31 & -26 & -48 \ 4 & 42 & -12 \ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 19 \ 35 \ -48 \end{bmatrix}$

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Question

Put the equations into proper matrix form.

Answer

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} a \ b \ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -34 & -28 & 3 \ -21 & 20 & -4 \ 39 & -48 & 8 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -41 \ 40 \ 3 \end{bmatrix}$

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Question

Put the equations into proper matrix form.

Answer

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} a \ b \ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -22 & 21 & 0 \ -18 & -6 & -26 \ -9 & -3 & -41 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -5 \ 11 \ 0 \end{bmatrix}$

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Question

Put the equations into proper matrix form.

Answer

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} a \ b \ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} 30 & -48 & -28 \ 21 & -46 & -5 \ 27 & 27 & -37 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 24 \ -32 \ -28 \end{bmatrix}$

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