Linear Algebra Level I
Discrete Mathematics Level I
Lin. Alg. and Discrete Math. Level II
Finance I
World Cup I
100
What is the determinant of this matrix?
-144
100
This law states, ¬(p^q)= p ∨ q.
What is DeMorgan's Law.
100
What is the determinant of this matrix?
-66
100
This is an agreement between you and a lender that allows you to borrow money to purchase or refinance a home and gives the lender the right to take your property if you fail to repay the money you've borrowed
What is Mortgage.
100
This team made history by defeating Spain and Germany in the group stage.
What is Japan.
200
These are the two conditions that prove a linear transformation
What are Scalar and Additive
OR
T(au)=aT(u)
T(u+v)=T(u)+T(v)
200
Given ∀x [P(x)-> Q(x)], the contrapositive, converse, and inverse statements are....
Contrapositive: ∀x [¬Q(x)-> ¬P(x)]
Converse: ∀x[Q(x)-->P(x)]
Inverse: ∀x[¬P(x)-> ¬Q(x)]
200
How can we find the inverse matrix?
What is put the matrix in an augmented matrix with the identity matrix to the right. Complete ERO and get the left side of the augmented matrix into RREF, to the best of your ability.
200
True/False/Sometimes: A Conventional mortgage usually has a rate that changes as the market interest rates change.
What is False.
200
This is the first African team to ever make it to the semifinals of the World Cup.
What is Morocco.
300
Find the diagonal matrix to this.
300
Prove that the sum of any two rational numbers is rational. (3 Minutes)
Proof: Let r and q be rational numbers. Let a, b, c, d ∈ ℤ such that r=a/b and q=c/d, where b, d ≠ 0.
r+q= a/b + c/d
= (ad + bc)/bd
Since ad+bc and bd ∈ ℤ, and bd≠0 (b≠, and d≠0), by definition, r+q is rational. QED.
300
CALCULATOR ACTIVE & DOUBLE POINTS!!!!
What are the eigenvalues of this matrix?
No need to give eigenvectors. Just eigenvalues are sufficient.
300
If a billing error occurs on a credit statement, a consumer has ____ days to notify the creditor.
What is 60.
300
This team is the defending champion of the World Cup.
What is France.
400
Given
400
Given A→ B, B→ C, and A.
Conclude C.
A→ B Given
A Given
B MP using Steps 1 and 2
B→ C Given
∴ C MP using Steps 3 and 4
400
DOUBLE + 1/2 POINTS!!!!!
Prove A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
Proof:
(⊆): Show that A ∪ (B ∩ C) ⊆ (A ∪ B) ∩ (A ∪ C),
if that x ∈ A ∪ (B ∩ C) → x ∈ (A ∪ B) ∩ (A ∪ C),
x ∈ A ∪ (B ∩ C) ↔ x ∈ A or x ∈ B ∩ C
Case 1: If x ∈ A, then certainly
x ∈ A ∪ B and x ∈ A ∪ C.
So, x ∈ (A ∪ B) ∩ (A ∪ C).
Case 2: If x ∈ B ∩ C, then x ∈ B and x ∈ C,
so x ∈ A ∪ B and x ∈ A ∪ C.
Hence, x ∈ (A ∪ B) ∩ (A ∪ C).
In all possible cases, x ∈ (A ∪ B) ∩ (A ∪ C), which proves the desired set inclusion.
(⊇): Show that A ∪ (B ∩ C) ⊇ (A ∪ B) ∩ (A ∪ C),
if that x ∈ (A ∪ B) ∩ (A ∪ C) → x ∈ A ∪ (B ∩ C),
x ∈ (A ∪ B) ∩ (A ∪ C) ↔ x ∈ (A ∪ B) or x ∈ B ∩ C and x ∈ (A ∪ C)
x ∈ (A ∪ B) ∩ (A ∪ C) ↔ x ∈ A or x ∈ B and x ∈ A or x ∈ C
Case 1: If x ∈ A, then x ∈ A ∪ x ∈ (B ∩ C).
Case 2: If x ∉ A, then, since it is true that [(x ∈ A or x ∈ B) and ( x ∈ A or x ∈ C)], it must be x ∈ B and x ∈ C, so x ∈ B ∩ C, in this case as well, x ∈ A ∪ (B ∩ C).
In all possible cases, x ∈ (A ∪ B) ∩ (A ∪ C) → x ∈ A ∪ (B ∩ C), which proves the desired reverse set inclusion.
QED.
400
This is is an arrangement in which the borrower agrees to share the increased value of the home with the lender when the home is sold.
What is Shared Appreciation Mortgage.
400
This major European team did not qualify for the World Cup.
What is Italy?
500
Assign each of these matrices as either REF or RREF
A - REF, B- RREF, C- RREF
(Bonus points if you can prove wrong)
500
Any mathematical system meets the following four requirements to be a group...
The set of elements is closed under the given operation.
An identity exists for the set under the given operation.
Every element has an inverse under the given operation.
The set of elements is associative under the given operation.
500
DOUBLE + 1/2 POINTS!!!!
Prove that √2 is irrational
Proof: Suppose, for the sake of contradiction, that √2 is a rational number. Then,
√2 = p/q where q ≠ 0
Furthermore, p and q are integers with no common factors. So,
2 = (p2/q2)
2q2 = p2
Since q2∈ Z, by def., we observe that p2 is an even integer. By the Theorem above, it follows that p is also even.
Therefore, there is an integer r such that p = 2r
2q2=4r2
q2=2r2
Since r2 is an integer, we see that q2 is an even integer. Since q2 is even, it follows that q is also even. However, p and q have no common factors, so they can’t both be even.
This is a contradiction, so we conclude that our original assumption must have been false and therefore √2 is an irrational number.
QED
500
Calculator Active Imagine that you would like to purchase a $275,000 home. Using 20% as a down payment (or $55,000), determine the monthly mortgage payment for your dream home using the loan terms. If there is a 20-year mortgage term with a 6% interest rate what is the Total Amount Paid Over Loan Term?
What is $378,276.60.
500
This team defeated Brazil but was eliminated.
What is Cameroon?