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# Matrix word problem: prices

## Video transcript

the price of things at two supermarkets are different in different cities toilet paper in Duluth Minnesota cost 399 a package while toilet paper in New York City costs 895 a package in Duluth toothpaste costs a dollar 95 a tube while in New York New York City it costs \$5.25 a tube the data for this can be encoded in the following grocery matrix so let's see if this makes sense so they have the price of toilet paper in Duluth 399 that's this right over here and then they have the price of toilet paper in New York at 895 so that's this right over here so this first row right over here this is the toilet paper row I'll just write TP for a short twilit that's the toilet paper row and this first column looks like it's Duluth while this second column looks like it's New York City New York City and let's see if that works out for the other data in Duluth toilet paper costs a dollar 95 it a toothpaste cost a dollar 95 a tube so this data right over here is right over here so this looks like the toothpaste row tooth toothpaste actually is also TP so I'll just write out tooth tooth so this is the toothpaste row this is toothpaste in Duluth the dollar 95 toothpaste in New York City 525 so that's how they have set up the data right over here which statements are true above the which statements are true about the above matrix select all that apply the following matrix can also be used to contain the same information as G and that's what's interesting about a matrix what we have right over here is a essentially an encapsulation of all of the data that we have in this upper paragraph and it's useful because a computer could make use of this data if it's as long as it knows what these rows and what these columns actually represent so the first thing they asked us is whether the following matrix can also be used to contain the same information so let's see this is the price of toilet paper in Duluth and this right over here the price of toilet paper in New York City so they have the exact same first row so I would say that looks like the toilet paper row and that would be Duluth column and this would be the New York City column but then if we define things that way then this would have to be the toothpaste row toothpaste row but the price of toothpaste in Duluth is not 525 and the price of toothpaste in New York City is not 195 so this one is not representing the same information as that up there they've gotten they've it's you know you can't just randomly order these around now you could represent it in other ways you could have another let's say I have the matrix a we could have picked to do something like this where we could have said well maybe this is the maybe this is the toothpaste column toothpaste column and maybe this is the toilet paper column and that this first row is New York City and the second row is Duluth you could have done something like this toothpaste in New York City was 525 toilet paper in New York City is 895 toothpaste in Duluth is 195 and toilet paper in Duluth is 399 so this would have been this this this matrix a that I've just constructed this does contain the same data because if we appropriately define our columns and rows to represent toothpaste or toilet paper in New York City or Duluth you can contain that information the problem with this one is it's not consistent this first row makes us think okay this must be the this must be the Duluth column this must be the New York City column and that the second row must be toothpaste it's the first row as toilet paper but then they got things mixed up if they switch these two things around then obviously you get the same matrix but then at least the data would have been consistent so I definitely would not say that this matrix contains the same information the second column represents the price of toothpaste in the two cities so the second column is this right over here no that's not the price of toothpaste in the two cities that's the price of the two different in New York City so I wouldn't I wouldn't check that one either element G 2 comma 1 is equal to 525 so when someone says so if you have the matrix and they give you 2 comma 1 these are the indices of the row and the column so this is says 2nd row first column so let's go there 2nd row so this is 1 2 second row first column is right over there so G 2 comma 1 is not Z 2 comma 1 is not 5 is not 5 25 so I wouldn't check that one either a change in the price of toilet paper in Duluth can be represented by the matrix so toilet paper in Duluth is this entry of our matrix right over there so a change in toilet paper in Duluth would represent a change in this 3.99 but they didn't change the 399 they changed the 975 the 975 would represent a change in the price of 12 paper in New York City so I wouldn't check that one either so I would only go only go with none of the none of the above