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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

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

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All Common Core: High School - Number and Quantity Resources

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Example Questions

Example Question #11 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Which of the following matrices represents the equations, $\displaystyle 1:10x-14y=-17$, and $\displaystyle 2:-9x+18y=-12$?

Possible Answers:

$\begin{bmatrix} -10 & -14 &-17 \\ -9& 18& -12 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -10 & -14 &-17 \\ -9& 18& -12 \end{bmatrix}$

$\begin{bmatrix} -10 & -14 &-17 \\ -9& -18& -12 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -10 & -14 &-17 \\ -9& -18& -12 \end{bmatrix}$

$\begin{bmatrix} 10 & -14 &-17 \\ -9& 18& -12 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 10 & -14 &-17 \\ -9& 18& -12 \end{bmatrix}$

$\begin{bmatrix} 10 & 14 &17 \\ 9& 18& -12 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 10 & 14 &17 \\ 9& 18& -12 \end{bmatrix}$

$\begin{bmatrix} 10 & 14 &-17 \\ 9& 18& -12 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 10 & 14 &-17 \\ 9& 18& -12 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 10 & -14 &-17 \\ -9& 18& -12 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 10 & -14 &-17 \\ -9& 18& -12 \end{bmatrix}$

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

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

where x_1,y_1 $\displaystyle x_1,y_1$, x_2,y_2 $\displaystyle x_2,y_2$ are coefficients of $\displaystyle x$ and $\displaystyle y$ in the first and second equation respectively. $\displaystyle c_1, c_2$ 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.

$\begin{bmatrix} 10 & -14 &-17 \\ -9& 18& -12 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 10 & -14 &-17 \\ -9& 18& -12 \end{bmatrix}$

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Example Question #12 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Which of the following matrices represents the equations, $\displaystyle 1:-x-14y=-1$, and $\displaystyle 2:-5x+8y=9$?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

It will look like this

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

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

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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

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #11 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Example Question #12 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

All Common Core: High School - Number and Quantity Resources

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