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 2x3 matrix. The order of the matrix lists 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 2,3? Well, 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 A12, that's in the first row, second column. So that has a value of 7. Element A21 is in the second row, first column. And so that has a value of 6. Let's consider another matrix. So let's say if we have matrix B and it has the numbers 4, 3, 7, negative 2, 5, 6, negative 4, 9, negative 3, 8, 1, and negative 7. What is the order of the matrix?
so let's start with the rules this is row 1 row 2 row 3 and then the columns column 1234 so the order of matrix being it's a 3x4 matrix it has three rows and four columns now identify elements B11, B23, B14, and B... 3, 4. Go ahead and identify these four elements. So this one is in the first row, first column. So that has a value of 4. Element B23, that is in the second row. third column so that has a value of negative 4 and Then element b14 is in the first row fourth column So that's equal to negative 2 And element B34 is in the third row, fourth column.
So it has a value of negative 7. 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 7, and 8. negative 5, 2, negative 1. And then we have matrix D, which contains the elements 4, 5, negative 2, 7, 3, and negative 6. And then we have matrix E, which contains one number, which is 8. Matrix F is going to have 7, 4, negative 5, and 11. And let's say matrix G has the numbers 3, 1, 7, 2, 6, negative 4, 9, 0, 3. 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 two-column matrix.
by two matrix now this is a square matrix because the number of rows and columns are the same in the square all sides of 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 2 by 4 matrix. And then for F, we have 1 row and there's 4 columns. So that's a 1 by 4 matrix. And finally, the last one, G.
That's another square matrix. As we can see, there's 3 rows and it has 3 columns. So that's a 3 by 3 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 7, 4, negative 3, and 5. what is the sum of matrix A and B so for adding 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 subtracting matrices as well So the first element, the one in the first row, first column, we need to add it with element B11 in the first row and the first column. They have to match. So this is going to be 2 plus 7. 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 5 plus negative 3 and these two numbers which are in the second row second column the result will remain in that position second row second column Now, 2 plus 7 is 9. 3 plus 4 is 7. 5 plus negative 3 is 2. Negative 4 plus 5 is 1. 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 4, what will you get?
4 times A, all you need to do is multiply every element by 4. So it's going to be 4 times 2, 4 times 3, 4 times 5, and 4 times negative 4. 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 2 minus 7, which is negative 5. 3 minus 4 is negative 1. 5 minus negative 3, or 5 plus 3, that's 8. Negative 4 minus 5 is negative 9. 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 PreCal, feel free to check the description section of this video. I'm going to post some links there. So thanks again for watching.