Linear Algebra

Question 1

Column views

Answer 1

x1w1 + x2w2 + x3*w3 (w’s are column vectors)

Question 2

내적

Answer 2

벡터 공간의 각도와 크기를 정해줌

Question 3

Let’s say there are n vectors.

These vectors are independent if and only if,

Answer 3

No linear combination of n-1 vectors can make the remaining vector

Question 4

Let’s say there are n n-dimensional vecotrs.

We can call these basis vectors if and only if?

Answer 4

1. The vectors are independent
2. Their linear combinations fill up the whole space
3. n*n matrix with the vecotrs as columns is invertible

Question 5

Subspace

Answer 5

Set of all linear combinations of vectors (including the whole space)

for n-dimension, origin, line, plane and the whole space

Question 6

Does associative property (결합법칙) hold for matrix multiplication?

Answer 6

Yes

Question 7

How do row and column operations differ?

Answer 7

Row on left, column on right.

Question 8

Explain Gauss-Jordan Elimination

Answer 8

[A I] => [I E’] using both downward and upward eliminations

Question 9

True or False,

R^t * R is symmetric

Answer 9

True

Question 10

What qualities should vector spaces satisfy?

Answer 10

1. Addition of two vectors should be defined.
2. Scalar multiplication should be defined.

Question 11

What are subspaces of R3?

Answer 11

1. R3 itself
2. Any plane going through the origin
3. Any line going through the origin
4. Origin

Question 12

Column space of matrix A (C(A)) is…

Answer 12

Subspace created by all the linear combinations of the columns of A

Question 13

Null space of matrix A is…

Answer 13

Subspace comprised of solutions to the equation Ax = 0

Question 14

Rank of a matrix is…

Answer 14

a number of pivots of a matrix