40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Matrices Lesson: MAT-2 Matrix Operations Matrix Operations Learning Outcome B-4 MAT-L1 Objectives: To perform basic Matrix operations.

40S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Matrices Lesson: MAT-2 Matrix Operations Matrix A represents the stock on March 1 st that three sporting goods stores had in dozens of tennis balls, baseballs, volleyballs, and golf balls. Matrix B represents the new supply of balls added to the inventory of each store during the month of March. Theory – Addition We can now determine the stock of balls in the stores available for sale in March by adding the elements of matrix A to the corresponding elements of matrix B. For example, A11 is added to B11. A12 to B12, and so on. Matrix C represents the stock after the new supply of balls has been added to the initial stock.

40S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Matrices Lesson: MAT-2 Matrix Operations Theory - Addition Note that when you add one matrix to another: the dimensions of the matrices must be the same each element from one matrix is added to the corresponding element of the other matrix the dimensions of the resulting matrix are the same as the dimensions of the initial matrices.

40S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Matrices Lesson: MAT-2 Matrix Operations During the month of March, the stores mentioned on the previous page sold the following number of balls, as indicated on Matrix D. The inventory available for sale during March from the previous page was Matrix C. The inventory of balls at the end of March can now be determined by subtracting the elements of matrix D from the corresponding elements of matrix C. For example, D 11 is subtracted from C 11, D 12 from C 12, and so on. Matrix E represents the inventory available for sale at the end of March. Theory - Subtraction

40S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Matrices Lesson: MAT-2 Matrix Operations Note that when you subtract one matrix from another: the dimensions of the matrices must be the same each element from the second matrix is subtracted from the corresponding element of the first matrix the dimensions of the resulting matrix are the same as the dimensions of the initial matrices Theory - Subtraction

40S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Matrices Lesson: MAT-2 Matrix Operations A scalar number is a number that indicates magnitude (size or quantity) only. For example, if you earn $7.50 per hour, then the number '7.50' is a scalar value. A local Manitoba travel agency has received information from an American travel agency about vacation trips to various parts of the United States. The table shows the prices in US dollars. Theory – Scalar Multiplication CaliforniaTexasFloridaHawaii 3 days days days The Manitoba travel agent needs to convert each price to Canadian dollars. The exchange rate is: $1.00 US = $1.48 Canadian

40S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Matrices Lesson: MAT-2 Matrix Operations The travel agent could multiply each number on the table to determine the prices in Canadian dollars. The same result could be obtained by writing the elements in the table in matrix form as Matrix A, and then multiplying the matrix by 1.48 to obtain Matrix B showing prices in Canadian dollars. Note that the common multiplier of 1.48 applies to each value in matrix A: Therefore, the results are: Theory – Scalar Multiplication

40S Applied Math Mr. Knight – Killarney School Slide 8 Unit: Matrices Lesson: MAT-2 Matrix Operations Matrix B represents the values of the trips in Canadian dollars. (The numbers in matrix B have been rounded to the nearest dollar.) Note the following: When multiplying a matrix by a number scalar, each element of the matrix is multiplied by the number. The dimensions of the final matrix are the same as the dimensions of the original matrix. As the matrices expand to contain more data, the amount of work doing tedious computations increases. We will reduce the amount of work by using IT (WinMat) to do the computations. Theory – Scalar Multiplication

40S Applied Math Mr. Knight – Killarney School Slide 9 Unit: Matrices Lesson: MAT-2 Matrix Operations Using the Matrices shown, identify which of the following operations are possible: A + B 3C C - B 2B – 5A Test Your Knowledge

40S Applied Math Mr. Knight – Killarney School Slide 10 Unit: Matrices Lesson: MAT-2 Matrix Operations Enter the Matrices shown into WinMat and perform the following operations: Using WinMat