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Common Core: High School - Number and Quantity : Vector & Matrix Quantities

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

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #7 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate $\left \| 10v\right \|$ , where v=<2,-1> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| 10\:v\right \|=5\sqrt{5}$ , Direction is the same as .

$\left \| 10\:v\right \|=10\sqrt{5}$ , Direction is the same as .

$\left \| 5\:v\right \|=-5\sqrt{5}$ , Direction is away from .

$\left \| 10\:v\right \|=-10\sqrt{5}$ , Direction is away from .

$\left \| 10\:v\right \|=10\sqrt{5}$ , Direction is away from .

Correct answer:

$\left \| 10\:v\right \|=10\sqrt{5}$ , Direction is the same as .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=10\cdot\sqrt{2^2+(-1)^2}=10\cdot\sqrt{4+1}=10\sqrt{5}$

As for the direction of the vector, since c>0 , the resulting vector in the same direction as the original vector .

See below for a picture.

Screen shot 2016 03 07 at 10.54.13 am

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Example Question #1 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate $\left \| 13v\right \|$ , where v=<0,-6> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| 13\:v\right \|=13$ , Direction is the same as .

$\left \| 13\:v\right \|=78$ , Direction is away from .

$\left \| 13\:v\right \|=-13$ , Direction is away from .

$\left \| 13\:v\right \|=78$ , Direction is the same as .

$\left \| 13\:v\right \|=-78$ , Direction is away from .

Correct answer:

$\left \| 13\:v\right \|=78$ , Direction is the same as .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=13\cdot\sqrt{0^2+6^2}=13\cdot\sqrt{0+36}=13\sqrt{36}=13\cdot6=78$

As for the direction of the vector, since c>0 , the resulting vector will be in the same direction as the original vector .

See below for a picture.

Screen shot 2016 03 07 at 11.09.17 am

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Example Question #9 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate $\left \| 11v\right \|$ , where v=<5,-1> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| 11\:v\right \|=11\sqrt{26}$ , Direction is the same as .

$\left \| 11\:v\right \|=\sqrt{26}$ , Direction is the same as .

$\left \| 11\:v\right \|=11\sqrt{26}$ , Direction is away from .

$\left \| 11\:v\right \|=-\sqrt{26}$ , Direction is away from .

$\left \| 11\:v\right \|=-11\sqrt{26}$ , Direction is away from .

Correct answer:

$\left \| 11\:v\right \|=11\sqrt{26}$ , Direction is the same as .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=11\cdot\sqrt{5^2+(-1)^2}=11\cdot\sqrt{25+1}=11\sqrt{26}$

As for the direction of the vector, since c>0 , the resulting vector will be in the same direction as the original vector .

See below for a picture.

Screen shot 2016 03 07 at 11.45.20 am

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Example Question #10 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate $\left \| -12v\right \|$ , where v=<4,4> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| -12\:v\right \|=\sqrt{2}$ , Direction is the same as .

$\left \| -12\:v\right \|=48\sqrt{2}$ , Direction is away from .

$\left \| -12\:v\right \|=-48\sqrt{2}$ , Direction is away from .

$\left \| -12\:v\right \|=-\sqrt{2}$ , Direction is away from .

$\left \| -12\:v\right \|=48\sqrt{2}$ , Direction is the same as .

Correct answer:

$\left \| -12\:v\right \|=48\sqrt{2}$ , Direction is away from .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=12\cdot\sqrt{4^2+4^2}=12\cdot\sqrt{16+16}=12\sqrt{32}=48\sqrt{2}$

As for the direction of the vector, since c<0 , the resulting vector will be against the original vector .

See below for a picture.

Screen shot 2016 03 07 at 11.53.48 am

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Example Question #191 : High School: Number And Quantity

Calculate $\left \| -10v\right \|$ , where v=<-6,7> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| -10\:v\right \|=-\sqrt{85}$ , Direction is away from .

$\left \| -10\:v\right \|=-10\sqrt{85}$ , Direction is away from .

$\left \| -10\:v\right \|=10\sqrt{85}$ , Direction is the same as .

$\left \| -10\:v\right \|=10\sqrt{85}$ , Direction is away from .

$\left \| -10\:v\right \|=\sqrt{85}$ , Direction is the same as .

Correct answer:

$\left \| -10\:v\right \|=10\sqrt{85}$ , Direction is away from .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=10\cdot\sqrt{(-6)^2+7^2}=10\cdot\sqrt{36+49}=10\sqrt{85}$

As for the direction of the vector, since c<0 , the resulting vector will be against the original vector .

See below for a picture.

Screen shot 2016 03 07 at 12.02.14 pm

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Example Question #192 : High School: Number And Quantity

Calculate $\left \| 7v\right \|$ , where v=<8,6> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| 7\:v\right \|=70$ , Direction is away from .

$\left \| 7\:v\right \|=7$ , Direction is the same as .

$\left \| 7\:v\right \|=-7$ , Direction is away from .

$\left \| 7\:v\right \|=-70$ , Direction is away from .

$\left \| 7\:v\right \|=70$ , Direction is the same as .

Correct answer:

$\left \| 7\:v\right \|=70$ , Direction is the same as .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=7\cdot\sqrt{8^2+6^2}=7\cdot\sqrt{64+36}=7\sqrt{100}=7\cdot10=70$

As for the direction of the vector, since c>0 , the resulting vector will be in the same direction as the original vector .

See below for a picture.

Screen shot 2016 03 07 at 12.10.09 pm

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Example Question #1 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Which of the following matrices represents the equations, 1:10x-4y=7 , and 2:-7x+5y=-10 ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 x_1,y_1 , x_2,y_2 are coefficients of and in the first and second equation respectively. 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.

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

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Example Question #2 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Which of the following matrices represents the equations, 1:-20x-8y=9 , and 2:-13x+18y=14 ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

It will look like this

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

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

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Example Question #194 : High School: Number And Quantity

Which of the following matrices represents the equations, 1:-15x-3y=-1 , and 2:7x-8y=0 ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

It will look like this

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

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

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Example Question #195 : High School: Number And Quantity

Which of the following matrices represents the equations, 1:16x+9y=11 , and 2:11x-18y=17 ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

It will look like this

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

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

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All Common Core: High School - Number and Quantity Resources

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Common Core: High School - Number and Quantity : Vector & Matrix Quantities

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 #7 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Example Question #1 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Example Question #9 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Example Question #10 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Example Question #191 : High School: Number And Quantity

Example Question #192 : High School: Number And Quantity

Example Question #1 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Example Question #2 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Example Question #194 : High School: Number And Quantity

Example Question #195 : High School: Number And Quantity

All Common Core: High School - Number and Quantity Resources

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