Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Give the $4 \times 4$ matrix that rotates points in $\mathbb{R}^{3}$ about the $z$ -axis through an angle of $-30^{\circ},$ and then translates by $\mathbf{p}=(5,-2,1)$

$\left[\begin{array}{cccc}{\frac{\sqrt{3}}{2}} & {\frac{1}{2}} & {0} & {5} \\ {-\frac{1}{2}} & {\frac{\sqrt{3}}{2}} & {0} & {-2} \\ {0} & {0} & {1} & {1} \\ {0} & {0} & {0} & {1}\end{array}\right]$

Algebra

Chapter 2

Matrix Algebra

Section 7

Applications to Computer Graphics

Introduction to Matrices

Campbell University

Oregon State University

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

00:38

Write the augmented matrix…

01:51

Use a graphing calculator …

00:44

02:50

Use matrix inversion to so…

00:30

00:34

00:33

03:48

03:27

Using the point $P(x, y)$ …

01:18

In Exercises $1-4,$ write …

So this question we first constructs the three by three matrix for the rotation. No, from the DAG girl that is looking at the door. A groom by the DAG room. We have duds defect. So do you want these roots instead? 30 degrees. So would I. The negative why exists on it stops odds stopping odds. The points, um co sign off minus 30 degrees. Sign off minus 30 degrees on zero. This is equality births three over itsu minus one over TSU on an zero similarly defect. So it to he's roots. It said Discredited 60 degrees because it's going toward the positive X exists. If you look at the diagram, stop on it stops arts stopping ads at the points course sign of 60 degrees sign of 60 degrees, another zero. And then this is just 1/4 1 of its suit words. Three over to sue under zero and, lastly, defect. So eat three e three. He's not changed by the rotation is not changed by the rotation because it is already on the Z exists on day recalled on the question Is accident goes to rotate about the exits, so since it the reserve that is the exists. The Vector eatery is not changed by the rotation. This implies that if we bring all this together, the Matrix for rotation is given by a, which is a quote. So the 1st 1 is what's three over to sue, minus one over to sue and zero. Then eat to give us one more word. Sue for three over two and zero and that Peter is unchanged. So this implies that's in Virginia's coordinates. In more Gina's coordinates. Dirac position is represented by by the mid tricks. A zero transpose zero wall, which is just This is my ace on average. Three over zoo one over TSU zero minus one over to sue Rude story over tsu 00 zero. Why are so? This is my age and I are zero 00 on then zero is there? Is there anyone? No for lying. Example. Seven B. In this section, we see that in a more Gina's coordinates. In a more genius coordinates The translation Victor. The translation of the translation by Vessel five minus two Comma Juan. He's represented Bi Metrics Juan 00001000010 And they add five minus 211 So, with this we know have that's this implies That's the complete transformation. Easy represented in Omagh. Gina's coordinates Ward needs by the metrics never moved out of the next page. So we're gonna multiply the translation, which is 1000 0100 00105 minus 211 on. Then we multiplied Thies. Bye, Woods. Theory of it. Sue minus one over. TSU 00 won over soon with three over Sue. 00 00100001 When you're multiplied this you're gonna have words three over the zoo minus one over TSU 00 won over TSU with three over 200 0010 five minus to want one on. This is the answer.

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, the absolute value or modulus |x| of a real number x is its …

Write the augmented matrix corresponding to the system of equations.$$\b…

Use a graphing calculator to solve each system of equations. Use matrix inve…

Use matrix inversion to solve the system of equations.$$\left\{\begin{ar…

Write the augmented matrix for each system of linear equations.$$\le…

Write the augmented matrix for each system of equations. $\begin{ali…

Write the augmented matrix for each system of linear equations.$$\begin{…

Using the point $P(x, y)$ and the rotation information, find the coordinates…

In Exercises $1-4,$ write the augmented matrix of the system.$$\begin{al…

01:45

Given $A=\left[\begin{array}{rr}{4} & {-6} \\ {-8} & {12} \\ {6} &am…

02:27

In Exercises $3-6,$ the vector $\mathbf{x}$ is in a subspace $H$ with a basi…

13:38

In Exercises $1-6,$ solve the equation $A \mathbf{x}=\mathbf{b}$ by using th…

Compute the determinants in Exercises $1-8$ using a cofactor expansion acros…

01:15

If $n \times n$ matrices $E$ and $F$ have the property that $E F=I$ then $E$…

03:02

Verify the boxed statement preceding Example 1

05:54

Let $\mathbf{v}_{1}=\left[\begin{array}{r}{2} \\ {3} \\ {-5}\end{array}\righ…

01:08

Suppose $A \mathbf{x}=\mathbf{b}$ has a solution. Explain why the solution i…

03:03

Describe the possible echelon forms of the matrix. Use the notation of Examp…

07:38

With $A$ and $\mathbf{p}$ as in Exercise $7,$ determine if $\mathbf{p}$ is i…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.