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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) = (x + 4)^2 - 3 $

03:21

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) = 16 - \frac{1}{4} x^2 $

02:02

In Exercises 7-12, match the quadratic function with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).] $ f(x) = 4 - (x - 2)^2 $

01:25

In Exercises 7-12, match the quadratic function with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).] $ f(x) = (x + 1)^2 - 2 $

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Okay, so this is going to be our fourth example of in vs of matrices, Siri's and the question says, determine whether matrix B is the inverse of Matrix A. So we have to to buy two matrices. Here's a two by two, and here is another two by two. So from here, we know that our process for checking whether something is a determine or the inverse of it is if we multiply A and B. So if this is a this is B, it should come out to a 1001 matrix. If we're doing two by twos just as a side note, if we're doing three by three, it should become 100010001 But since we have a two by two, we just have 1001 So let's go and try multiplying those two matrices and seeing what that becomes, because ideally, it should become, uh, to buy 10012 by two matrix. And that's how we'll know if Matrix B is the inverse of matrix A. So in this sense, the order does matter, because if Matrix B is the universe of matrix A. That means we're multiplying the original matrix by the inverse. So we have to do it this way. So we have to do three negative. One negative. 24 times to 5th. 1/5 or one tense and then 1/5 and then three tens. So think back to matrix multiplication. So what we do is we multiply three by two fists, so we're gonna do three by two fists, three times, two fists and then negative one times, 1/5. So, negative one. It's 1/5 in the first position. And then in our second position, I've got to do, Let's see. So then we've got to do this time is this. Plus this times this, which is going to become three times one tons plus negative one times three tons. So then the next step is to do this Times this. Plus this times this. That's negative. Two times, two fists plus four times one fist. Then lastly, landscape rid of some of this. Um Okay, so then we do this time. Is this across this times? This So we've got negative two times. One times plus four times 3/10. I'm gonna take this up here just to give myself some more space. So if I simplify this e got three times to fifth is six fist and then minus one times 1/5. This minus one fit. So then the 2nd 13 times one tons is three times plus three times 3/10 times negative. One is negative. Three tents and then the last one or the next one. Negative. Two times 2/5 is negative for over five and then four times 1/5 is plus 4/5 and then the last one. Negative. Two times one tense is negative. Two tons and then plus four times three tents is plus 12 tents. Then again, if I simplify it even further 6/5 minus 1/5 is 5/5 which is the same thing else. One three times minus three tons. Zero negative. 4/5 plus positive for fifth is zero, and then negative. Two tons plus 12 tons is 10/10, which is one. So we can notice that this becomes this, which is exactly what we want. And so because we have that 10012 by two matrix. We know that Matrix B is in fact, the inverse of a matrix a. So like I mentioned, warned earlier, You can't switch the order of them because then it would become a completely different thing. So if Matrix B is the inverse, that's going to be the second position. So keep that in mind because we have to have the Matrix multiplied by the inverse, not the inverse multiplied by the Matrix.

Introduction to Conic Sections

Discrete Maths

Introduction to Combinatorics and Probability

Introduction to Sequences and Series

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