Unit 2

Question 1

Diagonal

Answer 1

A square matrix with zeros everywhere but the diagonal

Question 2

Lower Triangular

Answer 2

zeros everywhere above the diagonal,
can still have zeros just not all zeroes

Question 3

upper triangular

Answer 3

A square matrix with zeros everywhere below the diagonal
can still have zeroes just not all zeros

Question 4

How to calculate determinent for 3 square systems

Answer 4

take product of diagonal

Question 5

What is determinent of identity matrix

Answer 5

1

Question 6

Determinent of a product det(a *b)

Answer 6

det(a)*det(b)

Question 7

solving for x with lower triangle

Answer 7

(entry in b -(knowns * x of prev))/coeff of diag

Question 8

solving x for upper triangle

Answer 8

same as lower but starting from bottom

Question 9

permutation matrix

Answer 9

an identity matrix with swapped rows

Question 10

how do permutation matrixes work

Answer 10

the location in permutation row is where original column switches to

Question 11

What are permutations used for

Answer 11

converting linear algebra equations into upper and lower triangles

Question 12

in factoring linear equations what is A equal to

Answer 12

LU

Question 13

process of solving factored equations

Answer 13

find the LU factorization of A
rewrite ax=b using L and U
let Ux=y
substritute Ux for Ly=b
solve for y using foreward sub
solve for x using backward sub Ux=y

Question 14

equations list for factoring

Answer 14

m.0 = A
m.1 = m.0 - 1/p.1 *c.1 *r.1
m.2 = m.1 - 1/p.2 *c.2 *r.2
m.n = m.n-1 - 1/p.n *c.n *r.n

Question 15

what is 1/p.i c.i

Answer 15

ith column of L

Question 16

what is r.i

Answer 16

ith row of U