MAT 2401 Linear Algebra 2.5 Applications of Matrix Operations
Chapter 2 Section 2.5 Reasoning With Properties of Algebra.
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Transcript of Chapter 2 Section 2.5 Reasoning With Properties of Algebra.
![Page 1: Chapter 2 Section 2.5 Reasoning With Properties of Algebra.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfd51a28abf838cad501/html5/thumbnails/1.jpg)
Chapter 2Section 2.5
Reasoning With Properties of Algebra
![Page 2: Chapter 2 Section 2.5 Reasoning With Properties of Algebra.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfd51a28abf838cad501/html5/thumbnails/2.jpg)
Algebraic Properties of Equality
• Let a, b,c be real numbers– Addition property of equality
• If a = b, then a + c = b + c
– Subtraction property of equality• If a = b, then a - c = b – c
– Multiplication property of equality• If a = b, then ac = bc
– Division property of equality• If a = b and c 0, then a c = b c
![Page 3: Chapter 2 Section 2.5 Reasoning With Properties of Algebra.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfd51a28abf838cad501/html5/thumbnails/3.jpg)
Algebraic Properties of Equality
• Let a, b,c be real numbers– Reflexive property of equality
• For any real number a, a = a
– Symmetric property of equality• If a = b, then b = a
– Transitive property of equality• If a = b and b = c, then a = c
– Substitution property of equality• If a = b, then a can be substituted for b in any
equation or expression
![Page 4: Chapter 2 Section 2.5 Reasoning With Properties of Algebra.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfd51a28abf838cad501/html5/thumbnails/4.jpg)
Use the property to complete the statement
1. Reflexive property of equality: mT = m T
2. Transitive property: If KL = MN and _____ = RW, then _____ MN KL = RW
3. Addition property of equality: If x = 5, then 17 + x = ______17 + 5
4. Symmetric property of equality: If BC = RL, then ______RL = BC
5. Substitution property of equality:
If mA = 45 and mB = mA + 90 then____mB = 45 + 90 = 135
6. Multiplication property of equality: If mA = 45, then _____
(mA) = 151
3
![Page 5: Chapter 2 Section 2.5 Reasoning With Properties of Algebra.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfd51a28abf838cad501/html5/thumbnails/5.jpg)
Complete the argument, giving a reason for each step
Addition Property of =Distributive Property
Subtraction Property of =
![Page 6: Chapter 2 Section 2.5 Reasoning With Properties of Algebra.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfd51a28abf838cad501/html5/thumbnails/6.jpg)
Complete the argument, giving a reason for each step
Addition Property of =Addition Property of =
Division Property of =
![Page 7: Chapter 2 Section 2.5 Reasoning With Properties of Algebra.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfd51a28abf838cad501/html5/thumbnails/7.jpg)
Complete the argument, giving a reason for each step
Substitution prop of =Segment Addition Postulate
Substitution property of =
![Page 8: Chapter 2 Section 2.5 Reasoning With Properties of Algebra.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfd51a28abf838cad501/html5/thumbnails/8.jpg)
Complete the argument, giving a reason for each step
a. Reflexive prop of =
Given
b. Addition property of =c. Angle Addition postulated. Angle Addition postulate
e. Substitution property of =
![Page 9: Chapter 2 Section 2.5 Reasoning With Properties of Algebra.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfd51a28abf838cad501/html5/thumbnails/9.jpg)
Complete the argument, giving a reason for each step
a. Definition linesGiven
b. Definition linesc. Substitution property of =
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HW #20Pg. 108-109 #1-29