Question

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

Answer 1

(a) A (b) A

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