Ch. 4 Determinants Flashcards Preview

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Flashcards in Ch. 4 Determinants Deck (14)
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1
Q

How to find the area of a parallelogram formed from the 2 vectors v, w

A

area = |det(vw)|

2
Q

How to find the area of a triangle with vertices a, b, and c

A

area = 1/2 |det(b-a, c-a)|

3
Q

How to find the area of a parallelepiped spanned by u, v, w

A

area = |det(u,v,w)|

4
Q

Definition of a permutation

A

A permutation of a non-empty set X is a bijection from X to itself. We put
SX = {bijections: X –> X}

5
Q

2 cycles are called disjoint if…

A

their members do not intersect

6
Q

How to compose 2 cycles σ o τ

A

Apply τ first and then σ

7
Q

What is the sign of a permutation

A

sgn(σ) = (-1)^(k-1)
where k is the number of numbers in that cycle
Then multiply the signs of the individual cycles together to get the overall sign

8
Q

What is the trace of a square matrix?

A

The sum of the entries in the diagonal

9
Q

How to find the adjoint matrix

A

First find the cofactor matrix, for each element, cover up its row and column, and calculate the determinant of the matrix left, then multiply by (-1)^(rs), where r and s are the row and column of the element
The adjoint is the transpose of this matrix

10
Q

For a matrix A, the element A12 represents…

A

The second element across in the first row

11
Q

det(a,b,c) =

A

a · (b x c)

12
Q

(v x w) · (v x w) =

A

|v x w|^2

13
Q

Write vector v in polar coordinates

A

v = R cosθ

sinθ

14
Q

What is a transposition?

A

A permutation of 2 elements