homework

1) For what value(s) of h the given system of linear

equations with augmented matrix A is consistent?

A = [ 𝟏 −𝟓 𝟓 𝟓 −𝟏𝟖 𝟒

−𝟏 𝟑 𝒉 ]

2) Construct a 6X6 system of linear equation with

(a) No solution (b) Unique solution (c) Infinitely

many solutions

3) Given the augmented matrix of a system of

equation [

1 2 3 4 5 2 4 6 8 10

−1 −2 −3 −4 −5 1 3 7 2 4

]

(a) Find the rank of the matrix. Indicate each step of the

necessary elementary row operations.

(b) Indicate any pivot column. Indicate any basic and/or

free variable.

(c) Indicate if no solution, unique solution or infinite

solution.

(d) Write the reduced row echelon form of the matrix.