Linear Algebra Chapter 1.4 - 1.9 Flashcards
What are 12 logic notations and what do they mean?
Check #1 on pg.15
What is #1 definition? Hint: subsets
Check #1 definition on page 15
Define propositional logic
It is a branch of mathematics that studies the value of logic statements
What are the main building blocks of any theorem?
Statements or propositions
What are five statement with p and q?
Check #2 on page 16
What are the three theorems and how do we prove them?
- “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.
What are five proof strategies and what are they about?
Check page 17-19
Prove theorem 1
Check theorem 1 on page 17
Prove number theory
Check number theory (theorem 2) on page.18
Prove theorem 3
Check theorem 3 on page. 18
Prove theorem 4.
Check theorem 4 on pg. 19
Prove the statement is false on page.19
Check counter examples on page 19- 20
What is 5# definition? Hint: expression and linear combination
Check 5#definition on pg.12
What is 6# properties and proof of the first properties? 2 things
Check 6# properties on backside of pg.13
What is 7# theorem and prove it
Check 7# theorem and proof on pg.14
What is 8# fact?
Check 8# fact on pg.14
What is 9# definition? Hint: homogeneous linear system
Check 9# definition on pg. 21
What is 10# theorem and prove it
Check 10# theorem on pg.21
What is 11# theorem. Hint: solution set and span of vectors
Check 11# theorem on backside of pg.21
What is 12# terminology? Hint: 5 things
Check 12# on pg.22
What is 13# definition?
Check 13# on backside of pg.22
What is 14# theorem? Hint: linear transformation
Check 14# on the backside of page.22
What is 15# facts?
Check 15# on pg.23
What is 16# theorem?
Check 16# theorem on pg.23
17# definition? Hint: Linear dependence
Check 17# in the backside of pg.24
18# theorem?
Check 18# on the backside of pg.24
19# definition? Hint: onto
Check 19# on pg. 25
20# definition? Hint: one-to-one
Check 20# on pg.25
21# theorem and proof?
Check 21# on the backside of pg.25
22# superposition principle
Check 22# on pg. 26
23# theorem and proof?
Check 23# ok pg.26
What are seven transformation with reflection, contraction and expansion?
Check pg. 74 and 75 in textbooks
What are two type of shear transformations and two projection transformation?
Check pg. 75 and 76 in the textbook
What does parametric form look like?
Check backside of pg.21
