systems of Linear Algebraic Equations

Systems of Linear Algebraic Equations

Exercise Set 1.

1. Find the solution set using Gauss elimination, and classify the result.

a.)

b.)

c.)

d.)

2. For what values of λ do the following systems admit non-trivial solutions? What happens when λ = 0?

a.)

b.)

Systems of Linear Algebraic Equations

Exercise Set 2.

1. Find the rank of the matrix (after reducing to row echelon form).

a.) A =

b.)

B =

c.)

C =

d.)

D =

e.)

E =

2. Using suitable row operations, check if the following pairs of matrices are row equivalent.

a.) and

b.) and