4. (25 Points) One of the most enduring and celebrated rock...

4. (25 Points) One of the most enduring and celebrated rock bands in music history is The Wandering Rocks. Four of their notable tracks are \"Leaping Larry Lightfoot\", \"Rumbling Cubes\", \"Sometimes It's Unattainable\", and \"Untamed Stallions\". The total duration of all four songs is 20.75 min. The collective playing time of Leaping Larry Lightfoot and Rumbling Cubes is equivalent to that of Sometimes It's Unattainable. Untamed Stallions is 2 min longer than Leaping Larry Lightfoot, and Sometimes It's Unattainable is twice as long as Rumbling Cubes. Compute the playing time of each track using the inverse matrix method.

Transcript

00:01 Okay, so for this problem, we're talking about rolling stone songs, and i'm going to let each of them represent the first letter of their songs.

00:07 Okay, so we have j.

00:11 It says that if we played all these songs, they'd have a total playing time of 20 .7 to 5 minutes.

00:17 So j is for jump and jack flash.

00:19 T is for t is for tumbling dice.

00:22 Y is for you can't always get what you want, and w is for wild horses.

00:28 So if we played all these songs together, we'd get 20 .75.

00:35 For my next equation, if i take j plus t, that would equal y.

00:44 Okay, because it says the playing time of jumping and tumbling is equal to that of you.

00:50 It also says that wild horses is, and that is indicates an equal sign.

00:57 And wild horses is two minutes longer than j.

01:04 And it also tells me that you can't always get what you want.

01:08 Nope.

01:09 And you can't always get what you want is twice as long as tumbling dice.

01:18 Okay.

01:19 So there's my four equations.

01:21 We need to manipulate these a little bit.

01:24 Because what we're going to do is we're going to first write the system of equations with all the variables on one side equalling the constants.

01:31 And then what we'll do is we'll write a matrix equation.

01:34 Okay.

01:34 The first equation is good to go because all the variables are on one side and all the constants are on the other side.

01:42 This next equation, i want to get all the variables on one side.

01:50 So the way that we can do that is subtract the y.

01:54 And when i do that, i'm going to line up my variables on my new system down here.

01:59 So j plus t minus y equals zero.

02:04 It just to kind of help me keep track of things...