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8 X 1 6 1 H! 7 i [ { 3 1 2 E 9 l HHF | 8 0 83 1 L 2 I W 1 9 1 1 1 [ HL 1 7 JiV 3 L 0 7 [ f 1 1 1 6 & 9 6 H 1 [...

Question

8 X 1 6 1 H! 7 i [ { 3 1 2 E 9 l HHF | 8 0 83 1 L 2 I W 1 9 1 1 1 [ HL 1 7 JiV 3 L 0 7 [ f 1 1 1 6 & 9 6 H 1 [

8 X 1 6 1 H! 7 i [ { 3 1 2 E 9 l HHF | 8 0 83 1 L 2 I W 1 9 1 1 1 [ HL 1 7 JiV 3 L 0 7 [ f 1 1 1 6 & 9 6 H 1 [



Answers

$$\left|\begin{array}{cccc} 1 & -1 & 8 & 4 \\ 2 & 6 & 0 & -4 \\ 2 & 0 & 2 & 6 \\ 0 & 2 & 8 & 0 \end{array}\right|$$

So on this problem, we're given this matrix and were asked to use matrix capability of a graphing utility to find the determinant. So I went to Desmond's dot com and went to math tools matrix calculator and got this matrix calculator. So I have a four x four matrix. So I go new matrix And I got four rows and four columns And the first entry is a zero and then a minus three in an eight and that too. And then eight one a minus one and six And then I -4 in a six. Mhm and zero and a nine. And then uh minus seven, two, zeros zero, zero and 14. They had dinner now to find the determiner of this, I use the D E T button right here go determine it a matrix A And there it is 7000 441 7441.

Notice Fine whether it is concerned, not so. Drop battle lane the y axis any object it got at once. So any land pedal to the Y axis if cutting graph points. So it is not difference and because for every below X we're getting to a low upward and downward. So port every. Have a look off X. There are toe value off Funston. Therefore, it is not fun. It isn't our defenses. And if you talk about Domine soared amendments all the way. Low Xer call the doorman sort of a woman. It's from minus four before. If you object all the way low. OPEC's carriageway often is from minus four to port on the range. Rains are often develop, which is from minus three to today, so this is stomach and range.

To find these two matrices together. Here. First thing we need to do is check the dimensions will work. Okay? First matrix we've got is two rows three columns. That's a two by three. The second matrix is a three row one column matrix. These inner two dimensions have to match which they do. That means is a resulting matrix will be dimension the outer dimensions. Okay, So we're gonna have to buy one. Matrix is our answer just two spots here. Okay, we'll fill in the first spot. This is gonna be row one. Column one. Okay, so everything in row one thinks everything in column one negative one times six plus zero times negative four plus seven. Thanks one. Okay, this should give us negative six plus zero plus seven. That should give us a one in that first little spot right there. Okay, The second guy this is gonna be row two column one. Okay, so we're gonna take everything in row two times that same column right there. So three times six less negative five that was negative for plus two times one spent 18 plus 20 plus two should give us 40. Okay? So one in the first row, 40 in the second round, and that is the result of this modification.

In this problem. We asked our ass to find the center of mass of this two dimensional system with the masses. 2 8 to 1 and four in the positions. Negative three negative. 100 And negative one, too. In order to find the center of mass, we first need to calculate the center mass in the ex direction, which we will do by calculating the moment in the UAE direction divided by the total mass. Once you've done that, we will calculate the, um, center of mass in the wind direction. Just calculate the moment in the ex direction of over the center of mess. Okay, So calculating Expert, um, the moment of wise calculating by multiplying the masses by the X coordinates. So we have eight times negative. Three plus one time, zero plus four times negative. One all over. The total mass, which is given by eight plus one is nine plus four gives us 13 doing some arithmetic. We can find out that eight times negative three is negative. 24 0 minus forgives us negative. 28 over 13. Now, to find the center of mass in the UAE direction, we're going to take the moment of X, which is the masses times there. Why Coordinates? So we're going to have eight times negative. One plus one time, zero plus four times two all over the total mass, which is still 13 here. Only two are particularly. Get negative 80 plus h, which gives us zero over 13 for our center of mass. Explore why BAR is given by the coordinate point. Negative 28 over 13 from a zero.


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