Problems 1 thru 4 use These matrices.
FIND THE DIMENSIONS OF MATRIX A THRU D WHICH MATRICES CAN BE ADDED? FIND THEIR SUM. 3. NAME TWO MATRICES THAT CANNOT BE ADDED. EXPLAIN 4. WHICH MATRIX CAN BE MULTIPLIED WITH MATRIC A. FIND THEIR PRODUCT 5. FIND THE DETERMINANT OF A.
EXAMPLE. Let’s say you’re in avid reader, and in June, July, and August you read fiction and non- fiction books, and magazines, both in paper copies and online. You want to keep track of how many different types of books and magazines you read, and store that information in matrices. Here is that information, and how it would look in matrix form:
We could also subtract matrices this same way. We can add matrices if the dimensions are the same; since the three matrices are all “3 by 2”, we can add them. For example, if we wanted to know the total number of each type of book/magazine we read, we could add each of the elements to get the sum: Thus we could see that we read 6 paper fiction, 9 online fiction, 6 paper non-fiction, 5 online non-fiction books, and 13 paper and 14 online magazines. We could also subtract matrices this same way.
If we wanted to see how many book and magazines we would have read in August if we had doubled what we actually read, we could multiply the August matrix by the number 2. This is called matrix scalar multiplication; a scalar is just a single number that we multiply with every entry. Note that this is not the same as multiplying 2 matrices together (which we’ll get to next):
Multiplying Matrices Multiplying matrices is a little trickier. First of all, you can only multiply matrices if the dimensions “match”; the second dimension (columns) of the first matrix has to match the first dimension (rows) of the second matrix, or you can’t multiply them. Think of it like the inner dimensions have to match, and the resulting dimensions of the new matrix are the outer dimensions. Here’s an example of matrices with dimensions that would work:
EXAMPLE # 2 MULTIPLICATION: Let’s say we want to find the final grades for 3 girls, and we know what their averages are for tests, projects, homework, and quizzes. We also know that tests are 40% of the grade, projects 15%, homework 25%, and quizzes 20%. Here’s the data we have:
Let’s organize the following data into two matrices, and perform matrix multiplication to find the final grades for Alexandra, Megan, and Brittney. To do this, you have to multiply in the following way:
The following matrix consists of a shoe store’s inventory of flip flops, clogs, and Mary Janes in sizes small, medium, and large The store wants to know how much their inventory is worth for all the shoes. Set up the matrix multiplication and then determine the total value of the inventory?
“S” REPRESENTS THE CONTENTS OF EACH PACKAGE. 6. VERDUGO HILLS JUGGLING CLUB IS SELLING 3 DIFFERENT PACKAGES OF JUGGLING EQUIPMENT AT THE EVER EXCITING VERDUGO DAY EVENT. PACKAGE 1 CONSISTS OF 3 JUGGLING BALLS AND 3 JUGGLING CLUBS BELOW, S REPRESENTS THE CONTENTS IN EACH PACKAGE. WHAT DOES THE MATRIX “S” REPRESENT? “S” REPRESENTS THE CONTENTS OF EACH PACKAGE.
6a. WHAT IS IN PACKAGE # 2?
MAKE A RANKED STEM AND LEAF PLOT FOR THE DATA 7. THE DATA BELOW REPRESENTS THE NUMBER OF TIMES THAT MR. WOODHOUSE 3 PUTTED IN A SINGLE ROUND OF GOLF AFTER REACHING THE GREEN IN THE APPROPRIATE AMOUNT OF STROKES TO GET A SCORE OF PAR. MAKE A RANKED STEM AND LEAF PLOT FOR THE DATA EXPLAIN HO TO FIND THE MEAN FIND THE MEDIAN FIND THE MODE MAKE A BOX AND WISKER PLOT FOR THE DATA FIND THE STANDARD DEVIATION OF THE DATA
9. SOLVE THE EQUATION
10. SOLVE FOR “x” IN THE EQUATION BELOW
11.
12. WRITE AN EQUATION OF A PARABOLA WHERE THE VERTEX IS A MAXIMUM AND THE MAXIMUM VALUE OF THE FUNCTION IS GREATER THAN 5
13. THE SUM OF THE INFINITE GEOMETRIC SERIES IS 6 AND THE FIRST TERM IS 10. FIND THE FIRST 5 TERMS OF THE SERIES.
FIND THE STANDARD DEVIATION OF THIS DATA. 14. FIND THE STANDARD DEVIATION OF THIS DATA. WHAT IS THE APPROXIMATE PERCENTAGE OF THE DATA THAT LIE BETWEEN 70 AND 115? C. FIND THA APPROXIMATE % OF THE DATA THAT BELOW 70.