1.5 Homogeneous Equations/1.4 Matrix Vector Products

Question 1

Homogeneous equations

Answer 1

a vector eqn of the form c1v1 + c2v2 + … + ckvk = 0 where v1, v2, …, vk belongs to all real numbers

Question 2

Are homogeneous eqn consistent? Explain

Answer 2

ALWAYS because the trivial solution is a solution

Question 3

Graphically, homogenous solutions must ___________ because _____________

Answer 3

go through the origin

of the trivial solution

Question 4

Matrix eqn

Answer 4

x1a1 + x2a2 +…+ xnan = b => Ax = b

Question 5

Matrix vector product

Answer 5

a linear combination of the columns of the matrix using the components of the vector as weights

Question 6

Let A be an m x n matrix if the following are equivalent

Answer 6

( 1 ) for all b in Rm, Ax = b is consistent

( 2 ) for all b in Rm, b is a linear combination of the columns of A

( 3 ) the columns of A span Rm

( 4 ) A has a pivot in every row