1. 3/6/2016Agenda Textbook / Web Based ResourceTextbook / Web Based Resource Operations with MatricesOperations with Matrices –Addition/Subtraction –Scalar Multiplication –Matrix Multiplication –Identity Matrix ClassworkClasswork HomeworkHomework INSERT HERE INSERT HERE

2. 3/6/2016 Operations with Matrices

3. 3/6/2016 By the end of the day: You should know how to: Add/Subtract two matricesAdd/Subtract two matrices Multiply a matrix by a scalarMultiply a matrix by a scalar Determine if two matrices can be multipliedDetermine if two matrices can be multiplied Determine the order of the product of two matricesDetermine the order of the product of two matrices Multiply two matricesMultiply two matrices Recognize the identity matrixRecognize the identity matrix

4. 3/6/2016 Matrix Add/Subtract Equality of Matrices – Two Matrices are equal if and only if they are the same size and their corresponding entries are equal Matrix Addition and Subtract Matrices must be the same size in order to be added or subtractedMatrices must be the same size in order to be added or subtracted Add/Subtract corresponding entriesAdd/Subtract corresponding entries Result should be a matrix the same size as the originalResult should be a matrix the same size as the original

5. 3/6/2016 Matrix Addition 2-4 57 54 -2-6 2-4 57 ++ ++ 54 -2-6 70 31 To Add Matrices, simply add the numbers that are in corresponding positions

6. 3/6/2016 Matrix Subtraction 2-4 57 54 -2-6 2-4 57 -- -- 54 -2-6 -3-8 713 To subtract matrices, simply subtract the numbers that are in corresponding positions

7. 3/6/2016 Matrix Addition and Subtraction You Try These on Your Own: 1.INSERT YOUR PROBLEMS HERE

8. 3/6/2016 Scalar Multiplication Multiplying an entire matrix by a factorMultiplying an entire matrix by a factor Multiply each entry by the Scalar factorMultiply each entry by the Scalar factor

9. 3/6/2016 Scalar Multiplication To multiply by a scalar, multiply each entry. 2-4 57 2-4 57 33333 6-12 1521

10. 3/6/2016Classwork 2) x = 5, y = -8 6)a) b)c)d) 4) x = -4, y = 9 8)a) b)c)d)

11. 3/6/2016 Matrix Multiplication Number of columns in first matrix must be the same as the number of rows in the second matrixNumber of columns in first matrix must be the same as the number of rows in the second matrix Answer will have same number of rows as the first matrix and the same number of columns as the second matrixAnswer will have same number of rows as the first matrix and the same number of columns as the second matrix Find each entry in the answer matrix by working across a row in the first matrix and down a column in the second matrix. Add the products together to get the entryFind each entry in the answer matrix by working across a row in the first matrix and down a column in the second matrix. Add the products together to get the entry

12. 3/6/2016 Matrix Multiplication = 2 x 3 3 x 2 2 x 2 3-254-3 13 5 -44 2 1, 11, 2 2, 12, 2 3-254-3 13 5 -44 2 1, 11, 2 2, 12, 2 = ++++ ++++ 2126 -23-2 To Multiply Matrices: Multiply Row by Column!!!

13. 3/6/2016 Matrix Multiplication You Try These on Your Own: 1.INSERT YOUR PROBLEMS HERE

14. 3/6/2016 Identity Matrix The Identity Matrix: Is a Square MatrixIs a Square Matrix Has entries of 1 across diagonalHas entries of 1 across diagonal Has entries of 0 everywhere elseHas entries of 0 everywhere else22)

15. 3/6/2016 Identity Matrix You Try These on Your Own: 1.INSERT YOUR PROBLEMS HERE

16. 3/6/2016 It’s the end of the day: Do you know how to: Add/Subtract two matrices?Add/Subtract two matrices? Multiply a matrix by a scalar?Multiply a matrix by a scalar? Determine if two matrices can be multiplied?Determine if two matrices can be multiplied? Determine the order of the product of two matrices?Determine the order of the product of two matrices? Multiply two matrices?Multiply two matrices? Recognize the identity matrix?Recognize the identity matrix?

17. 3/6/2016Homework Study: INSERT HERE Do: Read & Take Notes: INSERT HERE

18. 3/6/2016 Resource Credits Justin Bohannon Justin Bohannon Justin Bohannon