ðŸ’¬ ðŸ‘‹ Weâ€™re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

No Related Subtopics

Johns Hopkins University

Harvey Mudd College

Boston College

04:55

J H.

In Exercises 17-34, sketch the graph of the quadratic function without using a graphing utility. Identify the vertex, axis of symmetry, and x-intercept(s). $ f(x) = \frac{1}{2} x^2 - 4 $

06:07

In Exercises 13-16, graph each function. Compare the graph of each function with the graph of $ y = x^2 $. (a) $ f(x) = (x - 1)^2 $ (b) $ g(x) = (3x)^2 + 1 $ (c) $ h(x) = \left(\frac{1}{3} x^2 \right) - 3 $ (d) $ k(x) = (x + 3)^2 $

05:39

In Exercises 17-34, sketch the graph of the quadratic function without using a graphing utility. Identify the vertex, axis of symmetry, and x-intercept(s). $ g(x) = x^2 - 8 $

04:50

In Exercises 17-34, sketch the graph of the quadratic function without using a graphing utility. Identify the vertex, axis of symmetry, and x-intercept(s). $ f(x) = 1 - x^2 $

Create your own quiz or take a quiz that has been automatically generated based on what you have been learning. Expose yourself to new questions and test your abilities with different levels of difficulty.

Create your own quiz

Okay, so this is going to be the second example out off our in verses of matrices Siri's. And the question just says to find the inverse of the following matrix. So keep in mind that when we're looking for the inverse of a matrix, um, it's basically just the inverse is equal to one over the determinant. So the reciprocal of the determinant times the matrix Um, so we're going to switch these Jews now? It's gonna be d A and then for these two, this cross, we're not going to switch them. But we're gonna make them negative, so it's gonna be negative. Be negative c So, initially, if your matrix was a B C D, you essentially switch thes the order of those on the for these, you make them negative. So we already know right off the bat that for our matrix are inverse. We're gonna have one over the determinant times. So we're going to switch thes so it's gonna become negative one here, negative three here and for these, we're going to make them negative. So instead of positive one, we've got negative one, and instead of positive nine, we've got negative nine, so then from there, I still have to find the determinant of it in order for us to find the reciprocal of the determinant. And keep in mind that with the determinant of a two bunch of matrix, all we have to do is the a D minus specie from here. So it's negative. Three times negative, one minus one times nine So negative three times negative one is going to become positive. Three. Since the two negatives air going to combine into a positive. And then we subtract the one times nine, which is nine. That gives me negative six. So if I plug in this determinant right in here, so I'm just substituting that I got negative 16 times are determinant. Negative one negative, one negative. Nine. Negative three. So then, if I multiply those values negative 16 times negative one becomes positive. 16 Negative 16 times negative one Again, it's going to become a positive 16 Again negative. Nine times negative 16 is going to become three over to because it's 9/6, but 9/6 simplifies to 3/2. If we divide the top and bottom by three and then negative 16 times Negative. Three. It's becoming positive one half again because three negative three over negative six becomes one half. So I'm just simplifying that essentially. So here is our inverse matrix. So what you have to notice about this is that it also forms a two by two matrix. So the inverse matrix should be the same dimensions as the dimension as the dimensions of the matrix that you started with. And so, just to recap our steps, we have to basically find a way to fill in all of this information here. So you can start by finally the determinant and then taking the reciprocal of that. It doesn't matter where you start. So once you do that, you could also flip the order of this and then multiply. Or you can start by doing this the way I did, and then you find the determinant and then just simplified by multiplying

Introduction to Conic Sections

Discrete Maths

Introduction to Combinatorics and Probability

Introduction to Sequences and Series

03:06

04:45

02:49

01:49

01:46

01:59

02:17

03:02

02:55

02:21

03:14

02:28

06:22

05:00

03:47

03:10

05:38

01:51

04:28

05:15

05:16

01:39

01:42

01:36

02:08

02:41