MATH 225 Linear Algebra and Differential Equations Solved

Description

 

QUESTIONS:

1)( 20 pts.) For what values of k, if any, is the vector (k²,−3k,−2) ∈R³ in the span of {(1,2,3),(0,1,1),(1,3,4)}?

• Let

be given.

(a)( 10 pts.) Find the reduced echelon form of A.

(b)( 5 pts.) Find a basis for the Row(A).

(c)( 5 pts.) Find a basis for the Col(A).

(d)( 5 pts.) Find a basis for the Null(A).

(e)( 5 pts.) What are the rank and nullity of A?

• Let W be a subspace of R⁵ is spanned by the vectors v₁ = (1,3,−1,2,3), v₂ = (2,7,−2,5,2), v₃ = (1,4,−1,3,−1)

(a)( 10 pts.) Find a basis for W . What is the dim(W)?

(b)(10 pts.)Find a basis for the orthogonal complement W^⊥ of W. What is the dim(W^⊥) ?

IMPORTANT:

1.This project consists of 3 questions of different weights.

2.Don’t forget to write your Name, Lastname, Department, Section and Student ID on the 1st page of your project.

3.You must show all your work in well-organized English or mathematical sentences, and explain your reasoning carefully.

4.Your project must be hand written. The projects written by latex or word etc.

will not be accepted.

5. 5. You must submit your project as a 1 pdf file.