in this video we're going to focus on matrices now what exactly is a matrix a matrix is simply an array of numbers organized into rows and columns and first let's talk about the order of a matrix so consider matrix a and let's say it has the numbers 2 7 negative 4 6 3 and 5. what is the order of this matrix now this matrix has two rows and three columns now the rows are horizontal so this is the first row and this is the second row the columns are vertical this is the first column second third so there's two rows and three columns so this is considered a two by three matrix the order of the matrix list the rows first and then the number of columns now you need to be able to identify a specific element in a matrix for example what is element 2 comma 3 or sometimes it can be written as just element a23 so this is in matrix a and the first letter represents the row the second letter is the column so this is the first row this is the second row this is the first column second column third column so this element number five is in the second row third column so element a two three has a value of five now here's another one for you what's element a one two and also element a two one go ahead and identify the value of these elements so element a one two that's in the first row second column so that has a value of seven element a21 is in the second row first column and so that has a value of six let's consider another matrix so let's say if we have matrix b and it has the numbers four three seven negative two five six negative four nine negative three eight one and negative seven what is the order of the matrix so let's start with the rows this is row one row two row three and then the columns column one two three four so the order of matrix b it's a three by four matrix it has three rows and four columns now identify elements b11 b 2 3 b14 and b three four go ahead and identify these four elements so this one is in the first row first column so that has a value of four element b two three that is in the second row third column so that has a value of negative four and then element b14 is in the first row fourth column so that's equal to negative two and element b34 is in the third row fourth column so it has a value of negative seven so you need to be able to determine the order of the matrix and the value of every or any element in the matrix so what i'm going to do at this point is i'm going to give you a list of matrices and i want you to identify the order of each matrix so let's say if we have matrix c and it has the numbers 3 negative 5 2 negative 1 and then we have matrix d which contains the elements four five negative two seven three and negative six then we have matrix e which contains one number which is eight matrix f it's going to have seven four negative five and 11. and let's say matrix g has the numbers 3 1 7 2 six negative four nine zero three so identify the order of each matrix go ahead and try that let me just give you one more matrix h which is going to be 2 1 7 negative 3 6 negative 2 5 and 4. and also determine which of these matrices represents a square matrix so let's start with matrix c it has two rows and it has two columns so therefore it's a 2 by 2 matrix now this is a square matrix because the number of rows and columns are the same in the square all sides are the same now for matrix d we have three rows and two columns so this is going to be considered a three by two matrix so the order of the matrix is always going to be the number of rows times the number of columns now for matrix e it has one row and one column so because it only has one number it's a one by one matrix now for h there are two rows and there's four columns so this is a two by four matrix and then for f we have one row and there's four columns so that's a one by four matrix and finally the last one g that's another square matrix as we can see there's three rows and it has three columns so that's a three by three matrix so now you know how to determine the order of the matrix and you also know how to identify the elements within a matrix now let's focus on adding matrices so let's say if we have matrix a and it has the numbers 2 3 5 negative 4 and we have matrix b which is uh 7 4 negative 3 and 5. what is the sum of matrix a and b so if we add in those two matrices all we need to do is add the corresponding elements and by the way if you have a two by two matrix you can only add it to another two by two matrix the number of rows and columns must be the same when adding matrices or subtract the matrices as well so the first element the one in the first row first column we need to add it with uh element b11 in the first row in the first column they have to match so this is going to be 2 plus 7 and then we need to add these two so in the first row second column is going to be 3 plus 4 and then we're going to add those two numbers so that's going to be five plus negative three and these two numbers which are in the second row second column the result will remain in that position second row second column now two plus seven is nine three plus four is seven five plus negative three is two negative four plus five is one so this is the sum of matrix a and b and that's a simple way to add two matrices together it's not very complicated now let's say if you want to multiply matrix a by four what will you get four times a all you need to do is multiply every element by four so it's going to be four times two four times three four times five and four times negative four so then 4a is going to equal 8 12 20 and negative 16. so what about subtracting two matrices let's subtract matrix a and b so we're going to start with a and then subtract it by b so it's going to be 2 minus 7 3 minus 4 5 minus negative 3 and then negative 4 minus 5. so a minus b that's going to be two minus seven which is negative five three minus four is negative one five minus negative three or five plus three that's eight negative four minus five is negative nine and so that's the difference between the two matrices and that's it for this video if you want to find more videos on pre-cal feel free to check the description section of this video i'm gonna post some links there so thanks again for watching you