A is a 2*5 matrix with two pivot positions. (a) Does the equation Axequals=0 have a nontrivial solution? A. YesB. No (b) Does the equation Axequals=b have at least one solution for every possible b ? A. Yes

B. No

(a) A (b) A

Step-by-step explanation:

Ax = 0 does have a

non-trivial solution, option A

and Ax = b does have at least one solution for any

given b ... option A

For a 2*5 matrix with two pivot positions. If a matrix is in row-echelon form, then the first nonzero entry of each row is called a pivot, and the columns in which pivots appear are called pivot columns ...

For example

when Ax = 0

x₁ + 2x₂ + 4x₃ + 5x₄ - 2x₅ = 0

x₂ + 3x₃ + x₄ + 2x₅ = 0

The system of equation has a non trivial solution

And for any value of B, the system of equation have at the least one possible solution