EQ: What are the similarities and differences between matrices and real numbers?

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1 Unit 4 Lesson 1 Essentil Question Stndrds Objectives Vocbulry Mtrices Mtrix Opertions Wht re the similrities nd differences between mtrices nd rel numbers? M.ALGII.2.4

2 Unit 4: Lesson 1 Describe how you find your set in stdium when you go to sports gme or concert. Wht we re lerning tody: Wht mtrices re How to dd, subtrct nd multiply mtrices.

3 The Mtrix Mondy,

4 The Mtrix Mondy, M n 1,1 2,1,1 1,2 2,2 M n,2 L L O L 1, m 2, m M n, m

5 Mtrix (Plurl: Mtrices) A mtrix is rectngulr rry of numbers. Mtrices re nmed using cpitl letters. Exmple: A =

6 The Mtrix Mondy, Row 1 Row 2 Row n M n 1,1 2,1,1 1,2 2,2 M n,2 L L O L 1, m 2, m M n, m

7 The Mtrix Column 1 Column 2 Column m Mondy, M n 1,1 2,1,1 1,2 2,2 M n,2 L L O L 1, m 2, m M n, m

8 Dimensions of Mtrix Mondy, The dimensions of mtrix re the number of rows nd the number of columns in the mtrix. Exmples:

9 The Mtrix Mondy, Entry (Element) M n 1,1 2,1,1 1,2 2,2 M n,2 L L O L 1, m 2, m M n, m

10 Mtrix Entries AKA: Mtrix Elements The numbers inside mtrix re clled entries or elements. The loction or ddress of n entry is the number of the row nd column where the entry is locted. Exmple: The entry t row 2, column 3 is

11 Mtrix Equlity Two mtrices re equl if nd only if they hve identicl dimensions nd ll corresponding entries re equl. Exmple: =

12 Mtrix Addition nd Subtrction Mondy, It is only possible to dd or subtrct two mtrices, if they hve identicl dimensions. To find the sum, dd corresponding entries. To find the difference, subtrct corresponding entries. Exmples: = = Not Possible

13 Find the difference without clcultor: Mondy,

14 Use your clcultor to find ech sum or difference: 2 A = B = C 5 = 1 1) A + B 2) B + A 3) (A + B) + A 4) A + (B + A) 3 0 D =

15 Sclr Multipliction Mondy, A sclr is rel number. To multiply sclr by mtrix, multiply the sclr by every entry in the mtrix. Exmple: =

16 A = 2 4 Use your clcultor to find ech product: B = ) 5 B 2) -3 C 3) ½ D C 5 = D Mondy, =

17 Mtrix Multipliction Mondy, It is only possible to multiply two mtrices when the number of columns in the first mtrix is equl to the number of rows in the second mtrix. Exmple: Not Possible Possible

18 Mtrix Multipliction Mondy, The dimensions of the product of two mtrices will be the number of rows in the first mtrix nd the number of columns in the second mtrix. Exmple: = = 2 3

19 Mtrix 3 1 Multipliction = Row 1 Column

20 Mtrix 3 1 Multipliction = Row 1 Column

21 Mtrix 3 1 Multipliction = Row 1 Column 1 6

22 Mtrix 3 1 Multipliction = Row 1 Column

23 Mtrix 3 1 Multipliction = Row 1 Column

24 Mtrix 3 1 Multipliction = Row 1 Column

25 Mtrix 3 1 Multipliction = Row 1 Column

26 Mtrix 3 1 Multipliction = Row 1 Column

27 Mtrix 3 1 Multipliction = Row 1 Column

28 Mtrix 3 1 Multipliction = Row 2 Column

29 Mtrix 3 1 Multipliction = Row 2 Column

30 Mtrix 3 1 Multipliction = Row 2 Column

31 Mtrix 3 1 Multipliction = Row 2 Column

32 Mtrix 3 1 Multipliction = Row 2 Column

33 Mtrix 3 1 Multipliction = Row 2 Column

34 Mtrix 3 1 Multipliction = Row 2 Column

35 Mtrix 3 1 Multipliction = Row 2 Column

36 Mtrix 3 1 Multipliction = Row 2 Column

37 Mtrix 3 1 Multipliction =

38 =

39 A = 2 4 Use your clcultor to find ech product: B = ) C D 2) D C 3) D A 4) A C 5) C A 3 1 C 5 = D Mondy, =

40 Worksheet: Multiplying Mtrices #1

41 Worksheet: Multiplying Mtrices #2

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