Matrix Representation of Linear Equations: CCSS.Math.Content.HSA-REI.C.8

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Algebra › Matrix Representation of Linear Equations: CCSS.Math.Content.HSA-REI.C.8

Questions 1 - 10

Put the equations into proper matrix form.

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

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

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

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

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

Explanation

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.

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

Put the equations into proper matrix form.

$\begin{bmatrix} -31 & -26 & -48 \ 4 & 42 & -12 \ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 19 \ 35 \ 10 \end{bmatrix}$

$\begin{bmatrix} -31 & 4 & 36 \ -26 & 42 & 29 \ -48 & -12 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 19 \ 35 \ 10 \end{bmatrix}$

$\begin{bmatrix} -31 & -26 & -48 \ 4 & 42 & -12 \ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} y \ z \ x \end{bmatrix}=\begin{bmatrix} 19 \ 35 \ 10 \end{bmatrix}$

Explanation

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.

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

Put the equations into proper matrix form.

$\begin{bmatrix} -31 & -26 & -48 \ 4 & 42 & -12 \ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 19 \ 35 \ 10 \end{bmatrix}$

$\begin{bmatrix} -31 & 4 & 36 \ -26 & 42 & 29 \ -48 & -12 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 19 \ 35 \ 10 \end{bmatrix}$

$\begin{bmatrix} -31 & -26 & -48 \ 4 & 42 & -12 \ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} y \ z \ x \end{bmatrix}=\begin{bmatrix} 19 \ 35 \ 10 \end{bmatrix}$

$\begin{bmatrix} -26 & -31 & -48 \ 42 & 4 & -12 \ 49 & 29 & 36 \end{bmatrix} \cdot \begin{bmatrix} x \ z \ y \end{bmatrix}=\begin{bmatrix} 19 \ 35 \ 10 \end{bmatrix}$

$\begin{bmatrix} -31 & -26 & -48 \ 4 & -12 & 42 \ 36 & 49 & 29 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 19 \ 35 \ 10 \end{bmatrix}$

Explanation

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.

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

Put the equations into proper matrix form.

$\begin{bmatrix} -29 & -30 & 36 \ -14 & 48 & 35 \ -23 & 19 & -43 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -37 \ -37 \ -1 \end{bmatrix}$

$\begin{bmatrix} -29 & -14 & -23 \ -30 & 48 & 19 \ 36 & 35 & -43 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -37 \ -37 \ -1 \end{bmatrix}$

$\begin{bmatrix} -29 & -30 & 36 \ -14 & 48 & 35 \ -23 & 19 & -43 \end{bmatrix} \cdot \begin{bmatrix} y \ z \ x \end{bmatrix}=\begin{bmatrix} -37 \ -37 \ -1 \end{bmatrix}$

$\begin{bmatrix} -30 & -29 & 36 \ 48 & -14 & 35 \ -43 & 19 & -23 \end{bmatrix} \cdot \begin{bmatrix} x \ z \ y \end{bmatrix}=\begin{bmatrix} -37 \ -37 \ -1 \end{bmatrix}$

$\begin{bmatrix} -29 & -30 & 36 \ -14 & 35 & 48 \ -23 & -43 & 19 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -37 \ -37 \ -1 \end{bmatrix}$

Explanation

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.

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

Put the equations into proper matrix form.

$\begin{bmatrix} -22 & 21 & 0 \ -18 & -6 & -26 \ -9 & -3 & -41 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -5 \ 11 \ -37 \end{bmatrix}$

$\begin{bmatrix} -22 & -18 & -9 \ 21 & -6 & -3 \ 0 & -26 & -41 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -5 \ 11 \ -37 \end{bmatrix}$

$\begin{bmatrix} -22 & 21 & 0 \ -18 & -6 & -26 \ -9 & -3 & -41 \end{bmatrix} \cdot \begin{bmatrix} y \ z \ x \end{bmatrix}=\begin{bmatrix} -5 \ 11 \ -37 \end{bmatrix}$

$\begin{bmatrix} 21 & -22 & 0 \ -6 & -18 & -26 \ -41 & -3 & -9 \end{bmatrix} \cdot \begin{bmatrix} x \ z \ y \end{bmatrix}=\begin{bmatrix} -5 \ 11 \ -37 \end{bmatrix}$

$\begin{bmatrix} -22 & 21 & 0 \ -18 & -26 & -6 \ -9 & -41 & -3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -5 \ 11 \ -37 \end{bmatrix}$

Explanation

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.

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

Put the equations into proper matrix form.

$\begin{bmatrix} -47 & 3 & 37 \ 18 & 37 & -27 \ 31 & -20 & 29 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 2 \ 42 \ -28 \end{bmatrix}$

$\begin{bmatrix} -47 & 18 & 31 \ 3 & 37 & -20 \ 37 & -27 & 29 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 2 \ 42 \ -28 \end{bmatrix}$

$\begin{bmatrix} -47 & 3 & 37 \ 18 & 37 & -27 \ 31 & -20 & 29 \end{bmatrix} \cdot \begin{bmatrix} y \ z \ x \end{bmatrix}=\begin{bmatrix} 2 \ 42 \ -28 \end{bmatrix}$

$\begin{bmatrix} 3 & -47 & 37 \ 37 & 18 & -27 \ 29 & -20 & 31 \end{bmatrix} \cdot \begin{bmatrix} x \ z \ y \end{bmatrix}=\begin{bmatrix} 2 \ 42 \ -28 \end{bmatrix}$

$\begin{bmatrix} -47 & 3 & 37 \ 18 & -27 & 37 \ 31 & 29 & -20 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 2 \ 42 \ -28 \end{bmatrix}$

Explanation

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.

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

Put the equations into proper matrix form.

$\begin{bmatrix} -34 & 29 & -19 \ -48 & 9 & -13 \ -47 & 37 & -3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 40 \ 30 \ 23 \end{bmatrix}$

$\begin{bmatrix} -34 & -48 & -47 \ 29 & 9 & 37 \ -19 & -13 & -3 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 40 \ 30 \ 23 \end{bmatrix}$

$\begin{bmatrix} -34 & 29 & -19 \ -48 & 9 & -13 \ -47 & 37 & -3 \end{bmatrix} \cdot \begin{bmatrix} y \ z \ x \end{bmatrix}=\begin{bmatrix} 40 \ 30 \ 23 \end{bmatrix}$

$\begin{bmatrix} 29 & -34 & -19 \ 9 & -48 & -13 \ -3 & 37 & -47 \end{bmatrix} \cdot \begin{bmatrix} x \ z \ y \end{bmatrix}=\begin{bmatrix} 40 \ 30 \ 23 \end{bmatrix}$

$\begin{bmatrix} -34 & 29 & -19 \ -48 & -13 & 9 \ -47 & -3 & 37 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 40 \ 30 \ 23 \end{bmatrix}$

Explanation

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.

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

Put the equations into proper matrix form.

$\begin{bmatrix} 30 & -48 & -28 \ 21 & -46 & -5 \ 27 & 27 & -37 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 24 \ -32 \ 43 \end{bmatrix}$

$\begin{bmatrix} 30 & 21 & 27 \ -48 & -46 & 27 \ -28 & -5 & -37 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 24 \ -32 \ 43 \end{bmatrix}$

$\begin{bmatrix} 30 & -48 & -28 \ 21 & -46 & -5 \ 27 & 27 & -37 \end{bmatrix} \cdot \begin{bmatrix} y \ z \ x \end{bmatrix}=\begin{bmatrix} 24 \ -32 \ 43 \end{bmatrix}$

$\begin{bmatrix} -48 & 30 & -28 \ -46 & 21 & -5 \ -37 & 27 & 27 \end{bmatrix} \cdot \begin{bmatrix} x \ z \ y \end{bmatrix}=\begin{bmatrix} 24 \ -32 \ 43 \end{bmatrix}$

$\begin{bmatrix} 30 & -48 & -28 \ 21 & -5 & -46 \ 27 & -37 & 27 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 24 \ -32 \ 43 \end{bmatrix}$

Explanation

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.

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

Put the equations into proper matrix form.

$\begin{bmatrix} 39 & 34 & -35 \ 16 & 7 & 31 \ -48 & 29 & 44 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 2 \ -44 \ 37 \end{bmatrix}$

$\begin{bmatrix} 39 & 16 & -48 \ 34 & 7 & 29 \ -35 & 31 & 44 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 2 \ -44 \ 37 \end{bmatrix}$

$\begin{bmatrix} 39 & 34 & -35 \ 16 & 7 & 31 \ -48 & 29 & 44 \end{bmatrix} \cdot \begin{bmatrix} y \ z \ x \end{bmatrix}=\begin{bmatrix} 2 \ -44 \ 37 \end{bmatrix}$

$\begin{bmatrix} 34 & 39 & -35 \ 7 & 16 & 31 \ 44 & 29 & -48 \end{bmatrix} \cdot \begin{bmatrix} x \ z \ y \end{bmatrix}=\begin{bmatrix} 2 \ -44 \ 37 \end{bmatrix}$

$\begin{bmatrix} 39 & 34 & -35 \ 16 & 31 & 7 \ -48 & 44 & 29 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} 2 \ -44 \ 37 \end{bmatrix}$

Explanation

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.

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

Put the equations into proper matrix form.

$\begin{bmatrix} -34 & -28 & 3 \ -21 & 20 & -4 \ 39 & -48 & 8 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -41 \ 40 \ -36 \end{bmatrix}$

$\begin{bmatrix} -34 & -21 & 39 \ -28 & 20 & -48 \ 3 & -4 & 8 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -41 \ 40 \ -36 \end{bmatrix}$

$\begin{bmatrix} -34 & -28 & 3 \ -21 & 20 & -4 \ 39 & -48 & 8 \end{bmatrix} \cdot \begin{bmatrix} y \ z \ x \end{bmatrix}=\begin{bmatrix} -41 \ 40 \ -36 \end{bmatrix}$

$\begin{bmatrix} -28 & -34 & 3 \ 20 & -21 & -4 \ 8 & -48 & 39 \end{bmatrix} \cdot \begin{bmatrix} x \ z \ y \end{bmatrix}=\begin{bmatrix} -41 \ 40 \ -36 \end{bmatrix}$

$\begin{bmatrix} -34 & -28 & 3 \ -21 & -4 & 20 \ 39 & 8 & -48 \end{bmatrix} \cdot \begin{bmatrix} x \ y \ z \end{bmatrix}=\begin{bmatrix} -41 \ 40 \ -36 \end{bmatrix}$

Explanation

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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