Use Matrices to Represent and Manipulate Data: CCSS.Math.Content.HSN-VM.C.6

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Common Core: High School - Number and Quantity › Use Matrices to Represent and Manipulate Data: CCSS.Math.Content.HSN-VM.C.6

Questions 1 - 10

1

Which of the following matrices represents the equations, , and ?

$\begin{bmatrix} -20 & -8 &9 \ -13& 18& 14 \end{bmatrix}$

$\begin{bmatrix} 20 & -18 &9 \ -13& 18& 14 \end{bmatrix}$

$\begin{bmatrix} -20 & -8 &9 \ -18& 13& 14 \end{bmatrix}$

$\begin{bmatrix} -20 & -9 &18 \ -13& 8& 14 \end{bmatrix}$

$\begin{bmatrix} 20 & -8 &9 \ 13& 18& 14 \end{bmatrix}$

Explanation

To do this problem, all we need to do is put the coefficients for each variable into a matrix. The first column will be x values, 2nd column will be y values, and 3rd column will be what the equations are equal to.

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \ x_2& y_2& c_2 \end{bmatrix}$

where , are coefficients of and in the first and second equation respectively. refer to what the equations are equal to. So after placing the coefficients and what the equations are equal to in a matrix, it will look like the following.

$\begin{bmatrix} -20 & -8 &9 \ -13& 18& 14 \end{bmatrix}$

2

Which of the following matrices represents the equations, , and ?

$\begin{bmatrix} -15 & -3 &-1 \ 7& -8& 0 \end{bmatrix}$

$\begin{bmatrix} 15 & -3 &1 \ 7& -8& 0 \end{bmatrix}$

$\begin{bmatrix} -15 & 3 &1 \ 7& 8& 0 \end{bmatrix}$

$\begin{bmatrix} -15 & -3 &0 \ 7& -8& 0 \end{bmatrix}$

$\begin{bmatrix} 15 & 3 &1 \ 7& 8& 0 \end{bmatrix}$

Explanation

To do this problem, all we need to do is put the coefficients for each variable into a matrix. The first column will be x values, 2nd column will be y values, and 3rd column will be what the equations are equal to.

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \ x_2& y_2& c_2 \end{bmatrix}$

where , are coefficients of and in the first and second equation respectively. refer to what the equations are equal to. So after placing the coefficients and what the equations are equal to in a matrix, it will look like the following.

$\begin{bmatrix} -15 & -3 &-1 \ 7& -8& 0 \end{bmatrix}$

3

Which of the following matrices represents the equations, , and ?

$\begin{bmatrix} -18 & -6 &4 \ -4& -7& 15\end{bmatrix}$

$\begin{bmatrix} -18 & -6 &-4 \ -4& -7& -15\end{bmatrix}$

$\begin{bmatrix} 18 & -6 &4 \ -4& 7& 15\end{bmatrix}$

$\begin{bmatrix} 18 & 6 &4 \ 4& 7& 15\end{bmatrix}$

$\begin{bmatrix} -18 & -7 &4 \ -4& -6& 15\end{bmatrix}$

Explanation

To do this problem, all we need to do is put the coefficients for each variable into a matrix. The first column will be x values, 2nd column will be y values, and 3rd column will be what the equations are equal to.

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \ x_2& y_2& c_2 \end{bmatrix}$

where , are coefficients of and in the first and second equation respectively. refer to what the equations are equal to. So after placing the coefficients and what the equations are equal to in a matrix, it will look like the following.

$\begin{bmatrix} -18 & -6 &4 \ -4& -7& 15\end{bmatrix}$

4

Which of the following matrices represents the equations, , and ?

$\begin{bmatrix} 10 & -4 &7 \ -7& 5& -10 \end{bmatrix}$

$\begin{bmatrix} 10 & 5 &7 \ -7& -4& -10 \end{bmatrix}$

$\begin{bmatrix} 10 & 5 &-10 \ -7& -4& 7 \end{bmatrix}$

$\begin{bmatrix} -10 & 5 &7 \ -7& -4& 10 \end{bmatrix}$

$\begin{bmatrix} 10 & -7 &7 \ -7& 5& -10 \end{bmatrix}$

Explanation

To do this problem, all we need to do is put the coefficients for each variable into a matrix. The first column will be x values, 2nd column will be y values, and 3rd column will be what the equations are equal to.

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \ x_2& y_2& c_2 \end{bmatrix}$

where , are coefficients of and in the first and second equation respectively. refer to what the equations are equal to. So after placing the coefficients and what the equations are equal to in a matrix, it will look like the following.

$\begin{bmatrix} 10 & -4 &7 \ -7& 5& -10 \end{bmatrix}$

5

Which of the following matrices represents the equations, , and ?

$\begin{bmatrix} 11 & -15 &16 \ -14& 20& -18\end{bmatrix}$

$\begin{bmatrix} 11 & 15 &16 \ 14& 20& -18\end{bmatrix}$

$\begin{bmatrix} 11 & -15 &16 \ -14& 20& 18\end{bmatrix}$

$\begin{bmatrix} -11 & -15 &-16 \ -14& -20& -18\end{bmatrix}$

$\begin{bmatrix} 11 & 15 &16 \ 14& 20& 18\end{bmatrix}$

Explanation

To do this problem, all we need to do is put the coefficients for each variable into a matrix. The first column will be x values, 2nd column will be y values, and 3rd column will be what the equations are equal to.

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \ x_2& y_2& c_2 \end{bmatrix}$

where , are coefficients of and in the first and second equation respectively. refer to what the equations are equal to. So after placing the coefficients and what the equations are equal to in a matrix, it will look like the following.

$\begin{bmatrix} 11 & -15 &16 \ -14& 20& -18\end{bmatrix}$

6

Which of the following matrices represents the equations, , and ?

$\begin{bmatrix} -10 & 4 &9 \ -1& 16& 4 \end{bmatrix}$

$\begin{bmatrix} -10 & -4 &9 \ -1& -16& 4 \end{bmatrix}$

$\begin{bmatrix} -10 & 4 &-9 \ -1& -16& 4 \end{bmatrix}$

$\begin{bmatrix} -10 & 4 &9 \ -1& 16& -4 \end{bmatrix}$

$\begin{bmatrix} 10 & 4 &9 \ -1& 16& 4 \end{bmatrix}$

Explanation

To do this problem, all we need to do is put the coefficients for each variable into a matrix. The first column will be x values, 2nd column will be y values, and 3rd column will be what the equations are equal to.

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \ x_2& y_2& c_2 \end{bmatrix}$

where , are coefficients of and in the first and second equation respectively. refer to what the equations are equal to. So after placing the coefficients and what the equations are equal to in a matrix, it will look like the following.

$\begin{bmatrix} -10 & 4 &9 \ -1& 16& 4 \end{bmatrix}$

7

Which of the following matrices represents the equations, , and ?

$\begin{bmatrix} -1 & -14 &-1 \ -5& 8& 9 \end{bmatrix}$

$\begin{bmatrix} -1 & -14 &1 \ -5& 8& 9 \end{bmatrix}$

$\begin{bmatrix} 0 & -14 &-1 \ -5& 8& 9 \end{bmatrix}$

$\begin{bmatrix}0 & -1 &-1 \ -5& 8& 9 \end{bmatrix}$

$\begin{bmatrix} -1 & -14 &-11 \ -5& 8& 9 \end{bmatrix}$

Explanation

To do this problem, all we need to do is put the coefficients for each variable into a matrix. The first column will be x values, 2nd column will be y values, and 3rd column will be what the equations are equal to.

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \ x_2& y_2& c_2 \end{bmatrix}$

where , are coefficients of and in the first and second equation respectively. refer to what the equations are equal to. So after placing the coefficients and what the equations are equal to in a matrix, it will look like the following.

$\begin{bmatrix} -1 & -14 &-1 \ -5& 8& 9 \end{bmatrix}$

8

Which of the following matrices represents the equations, , and ?

$\begin{bmatrix} 16 & 9 &11 \ 11& -18& 17 \end{bmatrix}$

$\begin{bmatrix} 16 & 9 &11 \ 11& 18& 17 \end{bmatrix}$

$\begin{bmatrix} 16 & -18 &11 \ 11& 11& 17 \end{bmatrix}$

$\begin{bmatrix} 16 & 9 &17 \ 11& -18& 11 \end{bmatrix}$

$\begin{bmatrix} 16 & -9 &11 \ -11& -18& 17 \end{bmatrix}$

Explanation

To do this problem, all we need to do is put the coefficients for each variable into a matrix. The first column will be x values, 2nd column will be y values, and 3rd column will be what the equations are equal to.

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \ x_2& y_2& c_2 \end{bmatrix}$

where , are coefficients of and in the first and second equation respectively. refer to what the equations are equal to. So after placing the coefficients and what the equations are equal to in a matrix, it will look like the following.

$\begin{bmatrix} 16 & 9 &11 \ 11& -18& 17 \end{bmatrix}$

9

Which of the following matrices represents the equations, , and ?

$\begin{bmatrix} 19 & -8 &-20 \ 17& 4& 20 \end{bmatrix}$

$\begin{bmatrix} -19 & 8 &20 \ 17& -4& 20 \end{bmatrix}$

$\begin{bmatrix} 19 & -8 &-20 \ -17& 4& -20 \end{bmatrix}$

$\begin{bmatrix} -19 & -8 &-20 \ 17& -4& 20 \end{bmatrix}$

$\begin{bmatrix} 19 & -8 &-20 \ -17& -4& -20 \end{bmatrix}$

Explanation

To do this problem, all we need to do is put the coefficients for each variable into a matrix. The first column will be x values, 2nd column will be y values, and 3rd column will be what the equations are equal to.

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \ x_2& y_2& c_2 \end{bmatrix}$

where , are coefficients of and in the first and second equation respectively. refer to what the equations are equal to. So after placing the coefficients and what the equations are equal to in a matrix, it will look like the following.

$\begin{bmatrix} 19 & -8 &-20 \ 17& 4& 20 \end{bmatrix}$

10

Which of the following matrices represents the equations, , and ?

$\begin{bmatrix} -14 & -1 &-6 \ 14& 18& 17 \end{bmatrix}$

$\begin{bmatrix} -14 & -1 &-6 \ -14& 18& -17 \end{bmatrix}$

$\begin{bmatrix} 14 & 1 &6 \ 14& 18& 17 \end{bmatrix}$

$\begin{bmatrix} -14 & -1 &-6 \ -14& -18& -17 \end{bmatrix}$

$\begin{bmatrix} -14 & -1 &-6 \ 14& 18& 17 \end{bmatrix}$

Explanation

To do this problem, all we need to do is put the coefficients for each variable into a matrix. The first column will be x values, 2nd column will be y values, and 3rd column will be what the equations are equal to.

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \ x_2& y_2& c_2 \end{bmatrix}$

where , are coefficients of and in the first and second equation respectively. refer to what the equations are equal to. So after placing the coefficients and what the equations are equal to in a matrix, it will look like the following.

$\begin{bmatrix} -14 & -1 &-6 \ 14& 18& 17 \end{bmatrix}$

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