Linear Algebra Chapter 1.4 - 1.9

Question 1

What are 12 logic notations and what do they mean?

Answer 1

Check #1 on pg.15

Question 2

What is #1 definition? Hint: subsets

Answer 2

Check #1 definition on page 15

Question 3

Define propositional logic

Answer 3

It is a branch of mathematics that studies the value of logic statements

Question 4

What are the main building blocks of any theorem?

Answer 4

Statements or propositions

Question 5

What are five statement with p and q?

Answer 5

Check #2 on page 16

Question 6

What are the three theorems and how do we prove them?

Answer 6

• “if, then” theorem is a theorem of the form “If p, then q”. The proposition p is called premise or hypothesis and q is referred to as conclusion or thesis. We will prove this type of theorem using direct proof, proof by contraposition or proof by contradiction.
• “If and only if” theorem is a theorem of the form “p if and only if q”. It states that p and q are equivalent propositions and can be proved by splitting it into two “if, then” theorems.
• Equivalent statements is a generalization of the “if and only if” theorem is a theorem of the form “The following statements are equivalent: p, q, and r”. We can show this theorem by proving that “p->q”, “q->r” and “r->p” hold true.

Question 7

What are five proof strategies and what are they about?

Answer 7

Check page 17-19

Question 8

Prove theorem 1

Answer 8

Check theorem 1 on page 17

Question 9

Prove number theory

Answer 9

Check number theory (theorem 2) on page.18

Question 10

Prove theorem 3

Answer 10

Check theorem 3 on page. 18

Question 11

Prove theorem 4.

Answer 11

Check theorem 4 on pg. 19

Question 12

Prove the statement is false on page.19

Answer 12

Check counter examples on page 19- 20

Question 13

What is 5# definition? Hint: expression and linear combination

Answer 13

Check 5#definition on pg.12

Question 14

What is 6# properties and proof of the first properties? 2 things

Answer 14

Check 6# properties on backside of pg.13

Question 15

What is 7# theorem and prove it

Answer 15

Check 7# theorem and proof on pg.14

Question 16

What is 8# fact?

Answer 16

Check 8# fact on pg.14

Question 17

What is 9# definition? Hint: homogeneous linear system

Answer 17

Check 9# definition on pg. 21

Question 18

What is 10# theorem and prove it

Answer 18

Check 10# theorem on pg.21

Question 19

What is 11# theorem. Hint: solution set and span of vectors

Answer 19

Check 11# theorem on backside of pg.21

Question 20

What is 12# terminology? Hint: 5 things

Answer 20

Check 12# on pg.22

Question 21

What is 13# definition?

Answer 21

Check 13# on backside of pg.22

Question 22

What is 14# theorem? Hint: linear transformation

Answer 22

Check 14# on the backside of page.22

Question 23

What is 15# facts?

Answer 23

Check 15# on pg.23

Question 24

What is 16# theorem?

Answer 24

Check 16# theorem on pg.23

Question 25

17# definition? Hint: Linear dependence

Answer 25

Check 17# in the backside of pg.24

Question 26

18# theorem?

Answer 26

Check 18# on the backside of pg.24

Question 27

19# definition? Hint: onto

Answer 27

Check 19# on pg. 25

Question 28

20# definition? Hint: one-to-one

Answer 28

Check 20# on pg.25

Question 29

21# theorem and proof?

Answer 29

Check 21# on the backside of pg.25

Question 30

22# superposition principle

Answer 30

Check 22# on pg. 26

Question 31

23# theorem and proof?

Answer 31

Check 23# ok pg.26

Question 32

What are seven transformation with reflection, contraction and expansion?

Answer 32

Check pg. 74 and 75 in textbooks

Question 33

What are two type of shear transformations and two projection transformation?

Answer 33

Check pg. 75 and 76 in the textbook

Question 34

What does parametric form look like?

Answer 34

Check backside of pg.21