linear algebra

Math 2890_quiz 2

Show all work clearly and in detail.

1) Construct a 6 X 6 non zero matrix A and a vector b in 𝑅6 such that b is not

in the set spanned by the columns of A. (4 points)

2) The column of the matrix in reduced echelon form to the right span 𝑅4.

Find a column of the matrix that can be deleted and yet the remaining

matrix column still span 𝑅4. (5 points)

[

24 −14 22 −12 10 −18 8 −16 10 −6 −12 22 −14 0 −18 8 −12 20 −4 24

]

3) Describe the solutions of the first system of equations below

in parametric vector form. Provide a geometric comparison

with the solution set of the second system of equations

below. (6 points)

𝟓𝒙𝟏 + 𝟓𝒙𝟐 + 𝟏𝟎𝒙𝟑 = 𝟐𝟎

−𝟏𝟎𝒙𝟏 − 𝟏𝟎𝒙𝟐 − 𝟐𝟎𝒙𝟑 = −𝟒𝟎

−𝟐𝒙𝟐 + 𝟖𝒙𝟑 = 𝟒

𝟓𝒙𝟏 + 𝟓𝒙𝟐 + 𝟏𝟎𝒙𝟑 = 𝟎

−𝟏𝟎𝒙𝟏 − 𝟏𝟎𝒙𝟐 − 𝟐𝟎𝒙𝟑 = 𝟎

−𝟐𝒙𝟐 + 𝟖𝒙𝟑 = 𝟎